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Llvm loop terminology (and canonical forms) ¶, loop definition ¶.

Loops are an important concept for a code optimizer. In LLVM, detection of loops in a control-flow graph is done by LoopInfo . It is based on the following definition.

A loop is a subset of nodes from the control-flow graph (CFG; where nodes represent basic blocks) with the following properties:

The induced subgraph (which is the subgraph that contains all the edges from the CFG within the loop) is strongly connected (every node is reachable from all others).

All edges from outside the subset into the subset point to the same node, called the header . As a consequence, the header dominates all nodes in the loop (i.e. every execution path to any of the loop’s node will have to pass through the header).

The loop is the maximum subset with these properties. That is, no additional nodes from the CFG can be added such that the induced subgraph would still be strongly connected and the header would remain the same.

In computer science literature, this is often called a natural loop . In LLVM, a more generalized definition is called a cycle .

Terminology ¶

The definition of a loop comes with some additional terminology:

An entering block (or loop predecessor ) is a non-loop node that has an edge into the loop (necessarily the header). If there is only one entering block, and its only edge is to the header, it is also called the loop’s preheader . The preheader dominates the loop without itself being part of the loop.

A latch is a loop node that has an edge to the header.

A backedge is an edge from a latch to the header.

An exiting edge is an edge from inside the loop to a node outside of the loop. The source of such an edge is called an exiting block , its target is an exit block .

Important Notes ¶

This loop definition has some noteworthy consequences:

A node can be the header of at most one loop. As such, a loop can be identified by its header. Due to the header being the only entry into a loop, it can be called a Single-Entry-Multiple-Exits (SEME) region.

For basic blocks that are not reachable from the function’s entry, the concept of loops is undefined. This follows from the concept of dominance being undefined as well.

The smallest loop consists of a single basic block that branches to itself. In this case that block is the header, latch (and exiting block if it has another edge to a different block) at the same time. A single block that has no branch to itself is not considered a loop, even though it is trivially strongly connected.

In this case, the role of header, exiting block and latch fall to the same node. LoopInfo reports this as:

Loops can be nested inside each other. That is, a loop’s node set can be a subset of another loop with a different loop header. The loop hierarchy in a function forms a forest: Each top-level loop is the root of the tree of the loops nested inside it.

It is not possible that two loops share only a few of their nodes. Two loops are either disjoint or one is nested inside the other. In the example below the left and right subsets both violate the maximality condition. Only the merge of both sets is considered a loop.

It is also possible that two logical loops share a header, but are considered a single loop by LLVM:

which might be represented in LLVM-IR as follows. Note that there is only a single header and hence just a single loop.

The LoopSimplify pass will detect the loop and ensure separate headers for the outer and inner loop.

A cycle in the CFG does not imply there is a loop. The example below shows such a CFG, where there is no header node that dominates all other nodes in the cycle. This is called irreducible control-flow .

The term reducible results from the ability to collapse the CFG into a single node by successively replacing one of three base structures with a single node: A sequential execution of basic blocks, acyclic conditional branches (or switches), and a basic block looping on itself. Wikipedia has a more formal definition, which basically says that every cycle has a dominating header.

Irreducible control-flow can occur at any level of the loop nesting. That is, a loop that itself does not contain any loops can still have cyclic control flow in its body; a loop that is not nested inside another loop can still be part of an outer cycle; and there can be additional cycles between any two loops where one is contained in the other. However, an LLVM cycle covers both, loops and irreducible control flow.

The FixIrreducible pass can transform irreducible control flow into loops by inserting new loop headers. It is not included in any default optimization pass pipeline, but is required for some back-end targets.

Exiting edges are not the only way to break out of a loop. Other possibilities are unreachable terminators, [[noreturn]] functions, exceptions, signals, and your computer’s power button.

A basic block “inside” the loop that does not have a path back to the loop (i.e. to a latch or header) is not considered part of the loop. This is illustrated by the following code.

There is no requirement for the control flow to eventually leave the loop, i.e. a loop can be infinite. A statically infinite loop is a loop that has no exiting edges. A dynamically infinite loop has exiting edges, but it is possible to be never taken. This may happen only under some circumstances, such as when n == UINT_MAX in the code below.

It is possible for the optimizer to turn a dynamically infinite loop into a statically infinite loop, for instance when it can prove that the exiting condition is always false. Because the exiting edge is never taken, the optimizer can change the conditional branch into an unconditional one.

If a is loop is annotated with llvm.loop.mustprogress metadata, the compiler is allowed to assume that it will eventually terminate, even if it cannot prove it. For instance, it may remove a mustprogress-loop that does not have any side-effect in its body even though the program could be stuck in that loop forever. Languages such as C and C++ have such forward-progress guarantees for some loops. Also see the mustprogress and willreturn function attributes, as well as the older llvm.sideeffect intrinsic.

The number of executions of the loop header before leaving the loop is the loop trip count (or iteration count ). If the loop should not be executed at all, a loop guard must skip the entire loop:

Since the first thing a loop header might do is to check whether there is another execution and if not, immediately exit without doing any work (also see Rotated Loops ), loop trip count is not the best measure of a loop’s number of iterations. For instance, the number of header executions of the code below for a non-positive n (before loop rotation) is 1, even though the loop body is not executed at all.

A better measure is the backedge-taken count , which is the number of times any of the backedges is taken before the loop. It is one less than the trip count for executions that enter the header.

LoopInfo is the core analysis for obtaining information about loops. There are few key implications of the definitions given above which are important for working successfully with this interface.

LoopInfo does not contain information about non-loop cycles. As a result, it is not suitable for any algorithm which requires complete cycle detection for correctness.

LoopInfo provides an interface for enumerating all top level loops (e.g. those not contained in any other loop). From there, you may walk the tree of sub-loops rooted in that top level loop.

Loops which become statically unreachable during optimization must be removed from LoopInfo. If this can not be done for some reason, then the optimization is required to preserve the static reachability of the loop.

Loop Simplify Form ¶

The Loop Simplify Form is a canonical form that makes several analyses and transformations simpler and more effective. It is ensured by the LoopSimplify ( -loop-simplify ) pass and is automatically added by the pass managers when scheduling a LoopPass. This pass is implemented in LoopSimplify.h . When it is successful, the loop has:

A preheader.

A single backedge (which implies that there is a single latch).

Dedicated exits. That is, no exit block for the loop has a predecessor that is outside the loop. This implies that all exit blocks are dominated by the loop header.

Loop Closed SSA (LCSSA) ¶

A program is in Loop Closed SSA Form if it is in SSA form and all values that are defined in a loop are used only inside this loop.

Programs written in LLVM IR are always in SSA form but not necessarily in LCSSA. To achieve the latter, for each value that is live across the loop boundary, single entry PHI nodes are inserted to each of the exit blocks [ 1 ] in order to “close” these values inside the loop. In particular, consider the following loop:

In the inner loop, the X3 is defined inside the loop, but used outside of it. In Loop Closed SSA form, this would be represented as follows:

This is still valid LLVM; the extra phi nodes are purely redundant, but all LoopPass’es are required to preserve them. This form is ensured by the LCSSA ( -lcssa ) pass and is added automatically by the LoopPassManager when scheduling a LoopPass. After the loop optimizations are done, these extra phi nodes will be deleted by -instcombine .

Note that an exit block is outside of a loop, so how can such a phi “close” the value inside the loop since it uses it outside of it ? First of all, for phi nodes, as mentioned in the LangRef : “the use of each incoming value is deemed to occur on the edge from the corresponding predecessor block to the current block”. Now, an edge to an exit block is considered outside of the loop because if we take that edge, it leads us clearly out of the loop.

However, an edge doesn’t actually contain any IR, so in source code, we have to choose a convention of whether the use happens in the current block or in the respective predecessor. For LCSSA’s purpose, we consider the use happens in the latter (so as to consider the use inside) [ 2 ] .

The major benefit of LCSSA is that it makes many other loop optimizations simpler.

First of all, a simple observation is that if one needs to see all the outside users, they can just iterate over all the (loop closing) PHI nodes in the exit blocks (the alternative would be to scan the def-use chain [ 3 ] of all instructions in the loop).

Then, consider for example simple-loop-unswitch ing the loop above. Because it is in LCSSA form, we know that any value defined inside of the loop will be used either only inside the loop or in a loop closing PHI node. In this case, the only loop closing PHI node is X4. This means that we can just copy the loop and change the X4 accordingly, like so:

Now, all uses of X4 will get the updated value (in general, if a loop is in LCSSA form, in any loop transformation, we only need to update the loop closing PHI nodes for the changes to take effect). If we did not have Loop Closed SSA form, it means that X3 could possibly be used outside the loop. So, we would have to introduce the X4 (which is the new X3) and replace all uses of X3 with that. However, we should note that because LLVM keeps a def-use chain [ 3 ] for each Value, we wouldn’t need to perform data-flow analysis to find and replace all the uses (there is even a utility function, replaceAllUsesWith(), that performs this transformation by iterating the def-use chain).

Another important advantage is that the behavior of all uses of an induction variable is the same. Without this, you need to distinguish the case when the variable is used outside of the loop it is defined in, for example:

Looking from the outer loop with the normal SSA form, the first use of k is not well-behaved, while the second one is an induction variable with base 100 and step 1. Although, in practice, and in the LLVM context, such cases can be handled effectively by SCEV. Scalar Evolution ( scalar-evolution ) or SCEV, is a (analysis) pass that analyzes and categorizes the evolution of scalar expressions in loops.

In general, it’s easier to use SCEV in loops that are in LCSSA form. The evolution of a scalar (loop-variant) expression that SCEV can analyze is, by definition, relative to a loop. An expression is represented in LLVM by an llvm::Instruction . If the expression is inside two (or more) loops (which can only happen if the loops are nested, like in the example above) and you want to get an analysis of its evolution (from SCEV), you have to also specify relative to what Loop you want it. Specifically, you have to use getSCEVAtScope() .

However, if all loops are in LCSSA form, each expression is actually represented by two different llvm::Instructions. One inside the loop and one outside, which is the loop-closing PHI node and represents the value of the expression after the last iteration (effectively, we break each loop-variant expression into two expressions and so, every expression is at most in one loop). You can now just use getSCEV() . and which of these two llvm::Instructions you pass to it disambiguates the context / scope / relative loop.

“More Canonical” Loops ¶

Rotated loops ¶.

Loops are rotated by the LoopRotate ( loop-rotate ) pass, which converts loops into do/while style loops and is implemented in LoopRotation.h . Example:

is transformed to:

Warning : This transformation is valid only if the compiler can prove that the loop body will be executed at least once. Otherwise, it has to insert a guard which will test it at runtime. In the example above, that would be:

It’s important to understand the effect of loop rotation at the LLVM IR level. We follow with the previous examples in LLVM IR while also providing a graphical representation of the control-flow graphs (CFG). You can get the same graphical results by utilizing the view-cfg pass.

The initial for loop could be translated to:

_images/loop-terminology-initial-loop.png

Before we explain how LoopRotate will actually transform this loop, here’s how we could convert it (by hand) to a do-while style loop.

_images/loop-terminology-rotated-loop.png

Note two things:

The condition check was moved to the “bottom” of the loop, i.e. the latch. This is something that LoopRotate does by copying the header of the loop to the latch.

The compiler in this case can’t deduce that the loop will definitely execute at least once so the above transformation is not valid. As mentioned above, a guard has to be inserted, which is something that LoopRotate will do.

This is how LoopRotate transforms this loop:

_images/loop-terminology-guarded-loop.png

The result is a little bit more complicated than we may expect because LoopRotate ensures that the loop is in Loop Simplify Form after rotation. In this case, it inserted the %loop.preheader basic block so that the loop has a preheader and it introduced the %loop.exit basic block so that the loop has dedicated exits (otherwise, %exit would be jumped from both %latch and %entry, but %entry is not contained in the loop). Note that a loop has to be in Loop Simplify Form beforehand too for LoopRotate to be applied successfully.

The main advantage of this form is that it allows hoisting invariant instructions, especially loads, into the preheader. That could be done in non-rotated loops as well but with some disadvantages. Let’s illustrate them with an example:

We assume that loading from p is invariant and use(v) is some statement that uses v. If we wanted to execute the load only once we could move it “out” of the loop body, resulting in this:

However, now, in the case that n <= 0, in the initial form, the loop body would never execute, and so, the load would never execute. This is a problem mainly for semantic reasons. Consider the case in which n <= 0 and loading from p is invalid. In the initial program there would be no error. However, with this transformation we would introduce one, effectively breaking the initial semantics.

To avoid both of these problems, we can insert a guard:

This is certainly better but it could be improved slightly. Notice that the check for whether n is bigger than 0 is executed twice (and n does not change in between). Once when we check the guard condition and once in the first execution of the loop. To avoid that, we could do an unconditional first execution and insert the loop condition in the end. This effectively means transforming the loop into a do-while loop:

Note that LoopRotate does not generally do such hoisting. Rather, it is an enabling transformation for other passes like Loop-Invariant Code Motion ( -licm ).

Claimed by Sahil Arora (Fall 2016)

The Loop Rule, also known as Kirchhoff's Second Law, is a fundamental principle of electric circuits which states that the sum of potential differences around a closed circuit is equal to zero. More simply, when you travel around an entire circuit loop, you will return to the starting voltage. Note that is only true when the magnetic field is neither fluctuating nor time varying. If a changing magnetic field links the closed loop, then the principle of energy conservation does not apply to the electric field, causing the Loop Rule to be inaccurate in this scenario.

1.1 A Mathematical Model
1.2 A Computational Model
2.2 Middling
2.3 Difficult
3 Connectedness
5.1 Further Reading
5.2 External Links
6 References

The Main Idea

(The Energy Principle and the Loop Rule)

The loop rule simply states that in any round trip path in a circuit, Electric Potential equals zero. Keep in mind that this applies through ANY round trip path; there can be multiple round trip paths through more complex circuits. This principle deals with the conservation of energy within a circuit. Loop Rule and Node Rule are the two fundamental principles of electric circuits and are used to determine the behaviors of electric circuits. This principle is often used to solve for resistance or current passing through of light bulbs and other resistors, as well as the capacitance or charge of capacitors in a circuit.

A Visual Model

LOOP 1: [math]\displaystyle{ \Delta {V}_{AB} + \Delta {V}_{BC} + \Delta {V}_{CF} + \Delta {V}_{FA} = 0 }[/math]

LOOP 2: [math]\displaystyle{ \Delta {V}_{FC} + \Delta {V}_{CD} + \Delta {V}_{DE} + \Delta {V}_{EF} = 0 }[/math]

LOOP 3: [math]\displaystyle{ \Delta {V}_{AB} + \Delta {V}_{BC} + \Delta {V}_{CD} + \Delta {V}_{DE} + \Delta {V}_{EF} + \Delta {V}_{FA} = 0 }[/math]

To figure out the sign of the voltages, act as an observer walking along the path. Start at the negative end of the emf and continue walking along the path. The emf will be positive in the loop rule because you are moving from low to high voltage. Once you reach a resistor or capacitor, this will be negative in the loop rule equation because it is high to low voltage. Continue along the path until you return to the starting position.

LOOP 1: [math]\displaystyle{ emf - I_1R_1 = 0 }[/math]

LOOP 2: [math]\displaystyle{ -I_1R_1 + I_2R_2 = 0 }[/math]

LOOP 3: [math]\displaystyle{ emf - I_2R_2 = 0 }[/math]

A Mathematical Model

A mathematical representation is:

where n is the number of voltages being measured in the loop, as well as

along any closed path in a circuit.

A Computational Model

This is a pretty cool model of how the Loop Rule is applied and calculated. You can change the direction of the current as well as the voltage of the batteries. To turn off the voice, press the Audio Tutorial button. To test your knowledge, click on the Concept Questions and Notes buttons, they have some questions and useful information in them.

This is an online circuit simulator. It opens up with an LRC circuit that has current running through it. The graphs on the bottom show the voltage as the current runs through the circuit. You can see that after a full loop the voltage is 0, verifying the loop rule. You can make all sorts of different circuits and loops and see for yourself.

The circuit shown above consists of a single battery and a single resistor. The resistance of the wires is negligible for this problem.

If the [math]\displaystyle{ emf }[/math] is 5 V and the resistance of the resistor is 10 ohms, what is the current passing through the resistor?

Although we can solve this using the [math]\displaystyle{ V = IR }[/math] equation for the whole loop, let's examine this problem using the loop rule equation.

The loop rule equation would be [math]\displaystyle{ {V}_{battery} - {V}_{resistor} = 0 }[/math]

Since we know the [math]\displaystyle{ emf }[/math] of the battery we just need to find the potential difference through the resistor. For this we can use the equation of [math]\displaystyle{ V = IR }[/math] .

Thus we now have an loop rule equation of [math]\displaystyle{ emf - IR = 0 }[/math] From here it is a relatively simple process to find the current. We can rewrite the loop rule equation as [math]\displaystyle{ emf = IR }[/math] and then plug in 5 for the emf and 10 for the resistance, leaving us with I = .5 amperes.

The circuit shown above consists of a single battery, whose [math]\displaystyle{ emf }[/math] is 1.3 V, and three wires made of the same material, but having different cross-sectional areas. Let the length of the thin wires be [math]\displaystyle{ {L}_{thick} }[/math] and the length of the thin wire be [math]\displaystyle{ {L}_{thin} }[/math] Find a loop rule equation that starts at the negative end of the battery and goes counterclockwise through the circuit.

When beginning this problem, you must notice that the difference in cross-sectional areas affects the electric field in each wire. Because of this we will denote the electric field at D. as [math]\displaystyle{ {E}_{D} }[/math] and the electric field everywhere else as [math]\displaystyle{ {E}_{A} }[/math] . To begin we will go around the circuit clockwise and add up each component. First, we know that the [math]\displaystyle{ emf }[/math] of the battery is 1.3 V. Then, we will add up the potential voltage of each of the wires.

Remember that the electric potential of a wire is equal to the product of the electric field and the length of the wire. From this we can now find the potential difference of each section of the wires. The electric potential of location A - C is [math]\displaystyle{ {E}_{A} * {L}_{thick} }[/math] . This is the same for the electric potential of locations E - G of the wire. For the thin section of the wire, the electric potential is [math]\displaystyle{ {E}_{D} * {L}_{thin} }[/math] . From here we just go around the circuit counterclockwise and add each potential difference to the loop rule equation.

Thus we can find that a loop rule equation is: [math]\displaystyle{ emf - 2 ({E}_{A} * {L}_{thick}) - {E}_{D} * {L}_{thin} = 0 }[/math]

This can also be rewritten as: [math]\displaystyle{ emf = 2 ({E}_{A} * {L}_{thick}) + {E}_{D} * {L}_{thin} = 0 }[/math]

For the circuit above, imagine a situation where the switch has been closed for a long time. Calculate the current at a,b,c,d,e and charge Q of the capacitor. Answer these using [math]\displaystyle{ emf, {R}_{1}, {R}_{2}, and \space C }[/math]

First, write loop rule equations for each of the possible loops in the circuit. There are 3 loop equations that are possible.

[math]\displaystyle{ emf - {I}_{1}{R}_{1} - {I}_{2}{R}_{2} = 0 }[/math]

[math]\displaystyle{ emf - {I}_{1}{R}_{1} - Q/C = 0 }[/math]

[math]\displaystyle{ {I}_{2}{R}_{2} - Q/C = 0 }[/math]

From here, we can then solve for the current passing through a,b,d and e. We also know that the current passing through these points must be the same so [math]\displaystyle{ {I}_{1} = {I}_{2} }[/math]

[math]\displaystyle{ emf - {I}_{1}{R}_{1} - {I}_{1}{R}_{2} = 0 }[/math]

[math]\displaystyle{ emf = {I}_{1}({R}_{1} + {R}_{2}) = 0 }[/math]

[math]\displaystyle{ emf/({R}_{1} + {R}_{2}) = {I}_{1} }[/math]

So the current at a,b,d,e = [math]\displaystyle{ emf/({R}_{1} + {R}_{2}) }[/math]

You must also know that once a capacitor is charging for a long time, current no longer flows through the capacitor. We can then easily solve for c because since current is no longer flowing through the capacitor, the current at c = 0.

Lastly, we will use the loop rule equation of [math]\displaystyle{ {I}_{2}{R}_{2} - Q/C = 0 }[/math] to solve for Q.

[math]\displaystyle{ {I}_{2}{R}_{2} = Q/C }[/math]

[math]\displaystyle{ C*({I}_{2}{R}_{2}) = Q }[/math]

Since [math]\displaystyle{ {I}_{1} = {I}_{2} }[/math] , [math]\displaystyle{ C*({I}_{1}{R}_{2}) = Q }[/math]

We can plug in what we found [math]\displaystyle{ {I}_{1} }[/math] equals from before.

[math]\displaystyle{ C* (emf/({R}_{1} + {R}_{2})){R}_{2}) = Q }[/math]

Lastly, Q = [math]\displaystyle{ C* (emf/({R}_{1} + {R}_{2})){R}_{2} }[/math] and we have now solved the problem.

Current at a,b,d,e = [math]\displaystyle{ emf/({R}_{1} + {R}_{2}) }[/math]

Current at c = 0

Q = [math]\displaystyle{ C* (emf/({R}_{1} + {R}_{2})){R}_{2} }[/math]

Connectedness

The Loop Rule is simply an extension of the conservation of energy applied to circuits. Circuits are ubiquitous as they are featured in almost every technology today. Our understanding of these technologies is rooted in the empirical discoveries made in the mid 19th century, and further boosted by the the advancement of theoretical knowledge due to the likes of Faraday and Maxwell.

One interesting note about Loop Rule is that is does not apply universally to all circuits. In particular, AC (alternating current) circuits at high frequencies, have a fluctuating electric charge that changes direction. This causes the electric potential of a round trip path around the circuit to no longer be zero. However, DC (direct current) circuits, and low frequency circuits in general, still follow the loop rule.

The Loop Rule is formally known as the Kirchhoff Voltage Laws , named after Gustav Kirchhoff , the scientist who discovered and defined this fundamental concept of electric circuits. He discovered this during his time as a student at Albertus University of Königsberg in 1845. Kirchoff went on to explore the topics of spectroscopy and black body radiation after his graduation from Albertus. Nowadays, it is used very often in electrical engineering.

External Links

If you want to test your knowledge, Khan Academy's DC Circuit Analysis under the Electrical Engineering Topic is an excellent resource. There are questions, videos, and written explanations to help you understand not just the loop rule, but the node rule as well. Click here to access it.

Loop Rule - Boundless.com Textbook

Doc Physics Video Lecture

Doc Physics Worked Example

Bozeman Science Lecture

Dr. Nicholas Darnton's lecture notes
https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws#Kirchhoff.27s_voltage_law
https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-dc-circuit-analysis
Chabay, Ruth W. Matter and Interactions: Electric and Magnetic Interactions. John Wiley, 2015. Print.
http://www.ux1.eiu.edu/~cfadd/1360/28DC/Loop.html
http://higheredbcs.wiley.com/legacy/college/cutnell/0470223553/concept_sims/sim34/sim34.html
http://www.falstad.com/circuit/
Schuster, D. (Producer). (2013). Kirchhoff's Loop and Junction Rules Theory [Motion picture]. United States of America: YouTube.
Schuster, D. (Producer). (2013). Kirchhoff's Rules (Laws) Worked Example [Motion picture]. United States of America: YouTube.
Anderson, P. (Producer). (2015). Kirchoff's Loop Rule [Motion picture]. United States of America: YouTube.
Electric Fields and energy in circuits

Basics of Trips, Interlocks, Permissives & Sequences

Table of Contents

High level in a vessel initiates a trip system which stops the pump feeding that vessel, the pump will remain stopped even if the level in the vessel falls to a safe level.
The Trip must be ‘reset’ by the operator before the pump can be re-started.
The Trip can only be ‘reset’ if the level in the tank has fallen to a safe level.
Resetting the Trip will not cause the pump to automatically re-start, however it may be re-started by an operator action or a control system command e.g. part of a sequence.

Permissive:

Stop the feed pump
Close the filling valve
Stop the agitator.
Wait 30 seconds.
Open the discharge valve.
Low level in a vessel opens the filling valve.
The valve remains open until high level is detected.
On high level the valve closes.
The valve remains closed until low level is detected.
On low level the valve opens and the sequence it repeated.

Combined Functions:

7 thoughts on “Basics of Trips, Interlocks, Permissives & Sequences”

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Permissive start how it related to SIL and SIS

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Logic or programming in PLC is done using Ladder logic or other formats. In general there are some terms that are used is programming to identify how they will interact with other system.

These terms include:-

Permissives Protections Interlocks

Permissives are minimum perquisites that are required for drive or system to operate. Like lubrication system should be on before a drive starts etc.

Protection prevent a drive or logic from a harmful condition and start/ stop system to prevent human or mechanical damage. Like high current will trip a motor to prevent damage. These code act without any checks for permissives as they are typically a last resort kind of stuff.

Lastly Interlocks are code or conditions that are execute when another action happens and change how the drive or code was working to provide a smooth running process.

For example if 2 motors (say motor A & motor B) are there and only one is generally used but necessary 24 x 7. Then I will add an interlock in logic of motor A that if the other motor B turns off due to error then start drive A.

Interlocks are often used to start auxiliary equipment, standby drives, or to prevent starting of systems for smooth operations.

A key note is that Interlocks will require permissives to be followed, that is only interlock is not sufficient the permissives are also to be met.

Interlocks do jobs that can be executed by operator action also but provide some ease in operation and reduce human error.

Reference – Quora

Need help with understanding to interlock 2 different kinds of safety systems? for example 1 System with PLd & SIL2 safety and another with a safety relay system.

Thus to apply Kirchhoff’s voltage law correctly to a circuit, we must first understand the direction of the polarity and as we can see, the sign of the voltage drop across the resistive element will depend on the direction of the current flowing through it. As a general rule, you will loose potential in the same direction of current across an element and gain potential as you move in the direction of an emf source.

The direction of current flow around a closed circuit can be assumed to be either clockwise or anticlockwise and either one can be chosen. If the direction chosen is different from the actual direction of current flow, the result will still be correct and valid but will result in the algebraic answer having a minus sign.

To understand this idea a little more, lets look at a single circuit loop to see if Kirchhoff’s Voltage Law holds true.

A Single Circuit Loop

Kirchhoff’s voltage law states that the algebraic sum of the potential differences in any loop must be equal to zero as: ΣV = 0. Since the two resistors, R 1 and R 2 are wired together in a series connection, they are both part of the same loop so the same current must flow through each resistor.

Thus the voltage drop across resistor, R 1 = I*R 1 and the voltage drop across resistor, R 2 = I*R 2 giving by KVL:

We can see that applying Kirchhoff’s Voltage Law to this single closed loop produces the formula for the equivalent or total resistance in the series circuit and we can expand on this to find the values of the voltage drops around the loop.

Kirchhoff’s Voltage Law Example No1

Three resistor of values: 10 ohms, 20 ohms and 30 ohms, respectively are connected in series across an ideal 12 volt DC battery supply. Calculate: a) the total resistance, b) the circuit current, c) the current through each resistor, d) the voltage drop across each resistor, e) verify that Kirchhoff’s voltage law, KVL holds true.

a) Total Resistance (R T )

R T = R 1 + R 2 + R 3 = 10Ω + 20Ω + 30Ω = 60Ω

Then the total circuit resistance R T is equal to 60Ω

b) Circuit Current (I)

Thus the total circuit current I is equal to 0.2 amperes or 200mA

c) Current Through Each Resistor

The resistors are wired together in series, they are all part of the same loop and therefore each experience the same amount of current. Thus:

I R1 = I R2 = I R3 = I SERIES = 0.2 amperes

d) Voltage Drop Across Each Resistor

V R1 = I x R 1 = 0.2 x 10 = 2 volts

V R2 = I x R 2 = 0.2 x 20 = 4 volts

V R3 = I x R 3 = 0.2 x 30 = 6 volts

e) Verify Kirchhoff’s Voltage Law

Kirchhoff’s circuit loop.

We have seen here that Kirchhoff’s voltage law, KVL is Kirchhoff’s second law and states that the algebraic sum of all the voltage drops, as you go around a closed circuit from some fixed point and return back to the same point, and taking polarity into account, is always zero. That is ΣV = 0

The theory behind Kirchhoff’s second law is also known as the law of conservation of voltage, and this is particularly useful for us when dealing with series circuits, as series circuits also act as voltage dividers and the voltage divider circuit is an important application of many series circuits.

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In your circuit diagrams it is a mistake to fail to show batteries having an internal resistance. This gives a false view of the true situation. Your basic work on currents, potential differences and emf details is sound and good to follow. Thanks.

No, it is not. Batteries are taken as being ideal DC voltage sources, unless otherwise stated, for circuit analysis with zero internal resistance for ease of calculation and undestanding, (the same as for ideal zero-tolerance resistances). This assumption also implies an infinite current amount to and from any connected load. Typically, real or non-ideal batteries have negligibly small values of internal cell resistance (less than 0.5Ω) which would be added in series with the external load.

Then for Example No1 to which you refer. Assuming an internal battery resistance of about 0.3Ω’s. The total series circuit resistance would therefore be 60.3Ω, giving a closed-loop circuit current of 199mA, less than 1mA difference, and an internal voltage drop in the battery of less than 60mV. Clearly, the higher the load resistance value, the less effect a batteries internal resistance will have on any voltage or current calculations.

You can learn and understand more about the effects of internal resistance by reading our tutorial about Connecting Batteries Together .

I had both theories, electron flow in the NAVY (EM Nuclear) and positive hole flow as an Electrical Engineer. It took awhile to get use to positive flow after the NAVY. It is the standard in civilian engineering as started by Benjamin Franklin. By the time it was figured out that current is due to electron flow it was to late. So hard to change ie going metric still using lb, oz, mile, feet, inches….. go Newton.

I want more notes

Are you aware that you show current flowing from positive to negative in the circuits and that is exactly WRONG! Current in the battery flows from positive to negative but in the circuit it flows negative to positive.

No, electron flow is from a negative electrode to a positive electrode as a result of a potential difference between them. It is standard practice to say that current (measured in Amperes) flows from positive to negative. Its basic electrical theory.

very true Wayne

I understand it well

I want to be a part of this study

It’s so well explain. Thank you.

Electrica basic MCQ question

its helpfull i now understand more it enyoyable. i love to be part of this platform

How we can determine the voltage by two loops

Where can I find the information to use this as a source for one of my reports?

I love ❤ to be part of this educational forum..

nice presentation, it was helpful

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Kirchhoff’s Loop Rule Formula

As you all know, there are two Kirchhoff’s rules which are the junction rule and the loop rule. For instance, you see that a weightlifter needs to work to move a dumbbell from the ground (low potential) to his arm’s length (high potential). When he lets it go, gravity works to move it back to the ground. Thus, the dumbbell went in a loop. It began on the ground reached the maximum height then returned to the ground again. Thus, the net change in GPE ( gravitational potential energy ) is zero as there is neither gain nor loss of net energy. Similarly, we have a battery doing the same thing. However, in this case, it moves from negative to positive. Thus, this change in electric potential will be called voltage. We will study here about the kirchhoff’s loop rule formula.

Kirchhoff’s loop rule explains that the sum of all the electric potential differences nearby a loop is 0. Sometimes, we also refer to it as Kirchhoff’s voltage law or Kirchhoff’s second law. In other words, it states that the energy which the battery supplies get used up by all the other components in a loop.

It is so because energy cannot enter or leave a closed circuit. The rule is an application of the preservation of energy in terms of the electric potential difference $\Delta V$.

Get the huge list of Physics Formulas here

You will notice that any loop of a closed circuit consists of a number of circuit elements like batteries and resistors. The sum of the voltage differences throughout all these elements of circuits should be zero. We refer to this as Kirchhoff’s Loop Rule.

We measure the differences in voltage in Volts (V). When you have the current I in the loop given Amperes (A) and resistance of circuit elements in Ohms (Ω), then we can find the voltage difference across a resistor by using the formula V = IR.

Thus, you will get:

$\sum V$ = 0

$\sum V$ is the sum of voltage differences around a circuit loop which is 0

V is the voltage difference (Volts-V)

Solved Examples

Question- We have a circuit loop which comprises of 3 resistors and a voltage source which is the battery. The current in the loop is I = +4.00 A, in a clockwise direction. The voltage supplied by the battery is v b = 100.0 V. Furthermore, the resistance values of the two resistors out of the three are R 1 is 10. 0 Ω and R 2 is 8.00 Ω. You need to find the value of the resistor R 3 .

The Kirchhoff’s Loop Rule says that the sum of the voltage differences near the loop should be 0. Therefore, in order to find the sum, we need to choose the direction of travel. The direction of the positive current is said to be clockwise and thus, we will use this as the direction of travel so we can find out the sum. The voltage source i.e. the battery in the problem is said to have a positive voltage value in clockwise direction. The voltage drops in this direction due to the three resistors. We see that the magnitudes of the voltage drops are identical to the resistance multiplied by the current in the loop. Therefore, the sum of the voltage differences will be:

$\sum V$ = $V_{B} – 1R_{1} – 1R_{2} – 1R_{3}$ = 0

∴ $V_{B} – 1R_{1} – 1R_{2} – 1R_{3}$ = 0

(100.0 V) – (4.00 A) (10.0 Ω) – (4.00 A) (8.00 Ω) – (4.00 A) $R_{3}$ = 0

100.0 V – 40.0 V – 32.0 V – (4.00 A) $R_{3}$ = 0

28.0 V – (4.00 A) $R_{3}$ = 0

We can find the value of the third resistor by rearranging the formula:

∴ – (4.00 A) $R_{3}$ = -28.0 V

∴ (4.00 A) $ R_{3}$ = 28.0 V

∴ $R_{3}$ = $\frac{28.0V}{4.00A}$

∴ $R_{3}$ = 7.00 $\frac{V}{A}$

∴ $R_{3}$ = 7.00 Ω

Therefore, the value of resistor $R_{3}$ comes out as 7.00 Ω (Ohms).

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Physics Formulas

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5 responses to “Spring Potential Energy Formula”

Typo Error> Speed of Light, C = 299,792,458 m/s in vacuum So U s/b C = 3 x 10^8 m/s Not that C = 3 x 108 m/s to imply C = 324 m/s A bullet is faster than 324m/s

I have realy intrested to to this topic

m=f/a correct this

Interesting studies

It is already correct f= ma by second newton formula…

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2.1 Relative Motion, Distance, and Displacement

Section learning objectives.

By the end of this section, you will be able to do the following:

Describe motion in different reference frames
Define distance and displacement, and distinguish between the two
Solve problems involving distance and displacement

Teacher Support

The learning objectives in this section will help your students master the following standards:

(B) describe and analyze motion in one dimension using equations with the concepts of distance, displacement, speed, average velocity, instantaneous velocity, and acceleration;
(F) identify and describe motion relative to different frames of reference.

Section Key Terms

[BL] [OL] Start by asking what position is and how it is defined. You can use a toy car or other object. Then ask how they know the object has moved. Lead them to the idea of a defined starting point. Then bring in the concept of a numbered line as a way of quantifying motion.

[AL] Ask students to describe the path of movement and emphasize that direction is a necessary component of a definition of motion. Ask the students to form pairs, and ask each pair to come up with their own definition of motion. Then compare and discuss definitions as a class. What components are necessary for a definition of motion?

Defining Motion

Our study of physics opens with kinematics —the study of motion without considering its causes. Objects are in motion everywhere you look. Everything from a tennis game to a space-probe flyby of the planet Neptune involves motion. When you are resting, your heart moves blood through your veins. Even in inanimate objects, atoms are always moving.

How do you know something is moving? The location of an object at any particular time is its position . More precisely, you need to specify its position relative to a convenient reference frame . Earth is often used as a reference frame, and we often describe the position of an object as it relates to stationary objects in that reference frame. For example, a rocket launch would be described in terms of the position of the rocket with respect to Earth as a whole, while a professor’s position could be described in terms of where she is in relation to the nearby white board. In other cases, we use reference frames that are not stationary but are in motion relative to Earth. To describe the position of a person in an airplane, for example, we use the airplane, not Earth, as the reference frame. (See Figure 2.2 .) Thus, you can only know how fast and in what direction an object's position is changing against a background of something else that is either not moving or moving with a known speed and direction. The reference frame is the coordinate system from which the positions of objects are described.

[OL] [AL] Explain that the word kinematics comes from a Greek term meaning motion. It is related to other English words, such as cinema (movies, or moving pictures) and kinesiology (the study of human motion).

Your classroom can be used as a reference frame. In the classroom, the walls are not moving. Your motion as you walk to the door, can be measured against the stationary background of the classroom walls. You can also tell if other things in the classroom are moving, such as your classmates entering the classroom or a book falling off a desk. You can also tell in what direction something is moving in the classroom. You might say, “The teacher is moving toward the door.” Your reference frame allows you to determine not only that something is moving but also the direction of motion.

You could also serve as a reference frame for others’ movement. If you remained seated as your classmates left the room, you would measure their movement away from your stationary location. If you and your classmates left the room together, then your perspective of their motion would be change. You, as the reference frame, would be moving in the same direction as your other moving classmates. As you will learn in the Snap Lab , your description of motion can be quite different when viewed from different reference frames.

[BL] [OL] You may want to introduce the concept of a reference point as the starting point of motion. Relate this to the origin of a coordinate grid.

[AL] Explain that the reference frames considered in this chapter are inertial reference frames, which means they are not accelerating. Engage students in a discussion of how it is the difference in motion between the reference frame of the observer and the reference frame of the object that is important in describing motion. The reference frames used in this chapter might be moving at a constant speed relative to each other, but they are not accelerating relative to each other.

[BL] [OL] [Visual] Misconception: Students may assume that a reference frame is a background of motion instead of the frame from which motion is viewed. Demonstrate the difference by having one student stand at the front of the class. Explain that this student represents the background. Walk once across the room between the student and the rest of the class. Ask the student and others in the class to describe the direction of your motion. The class might describe your motion as to the right , but the student who is standing as a background to your motion would describe the motion as to the left . Conclude by reminding students that the reference frame is the viewpoint of the observer, not the background.

[BL] Have students practice describing simple examples of motion in the class from different reference frames. For example, slide a book across a desk. Ask students to describe its motion from their reference point, from the book's reference point, and from another student's reference point.

Looking at Motion from Two Reference Frames

In this activity you will look at motion from two reference frames. Which reference frame is correct?

Choose an open location with lots of space to spread out so there is less chance of tripping or falling due to a collision and/or loose basketballs.
1 basketball
Work with a partner. Stand a couple of meters away from your partner. Have your partner turn to the side so that you are looking at your partner’s profile. Have your partner begin bouncing the basketball while standing in place. Describe the motion of the ball.
Next, have your partner again bounce the ball, but this time your partner should walk forward with the bouncing ball. You will remain stationary. Describe the ball's motion.
Again have your partner walk forward with the bouncing ball. This time, you should move alongside your partner while continuing to view your partner’s profile. Describe the ball's motion.
Switch places with your partner, and repeat Steps 1–3.

Grasp Check

How do the different reference frames affect how you describe the motion of the ball?

The motion of the ball is independent of the reference frame and is same for different reference frames.
The motion of the ball is independent of the reference frame and is different for different reference frames.
The motion of the ball is dependent on the reference frame and is same for different reference frames.
The motion of the ball is dependent on the reference frames and is different for different reference frames.

Before students begin the lab, arrange a location where pairs of students can have ample room to walk forward at least several meters.

As students work through the lab, encourage lab partners to discuss their observations. In Steps 1 and 3, students should observe the ball move straight up and straight down. In Step 2, students should observe the ball in a zigzag path away from the stationary observer.

After the lab, lead students in discussing their observations. Ask them which reference frame is the correct one. Then emphasize that there is not a single correct reference frame. All reference frames are equally valid.

Links To Physics

History: galileo's ship.

The idea that a description of motion depends on the reference frame of the observer has been known for hundreds of years. The 17 th -century astronomer Galileo Galilei ( Figure 2.3 ) was one of the first scientists to explore this idea. Galileo suggested the following thought experiment: Imagine a windowless ship moving at a constant speed and direction along a perfectly calm sea. Is there a way that a person inside the ship can determine whether the ship is moving? You can extend this thought experiment by also imagining a person standing on the shore. How can a person on the shore determine whether the ship is moving?

Galileo came to an amazing conclusion. Only by looking at each other can a person in the ship or a person on shore describe the motion of one relative to the other. In addition, their descriptions of motion would be symmetric or opposite. A person inside the ship would describe the person on the land as moving past the ship. The person on shore would describe the ship and the person inside it as moving past. Galileo realized that observers moving at a constant speed and direction relative to each other describe motion in the same way. Galileo had discovered that a description of motion is only meaningful if you specify a reference frame.

I would see the train as moving past me, and a person on the train would see me as stationary.
I would see the train as moving past me, and a person on the train would see me as moving past the train.
I would see the train as stationary, and a person on the train would see me as moving past the train.
I would see the train as stationary, and a person on the train would also see me as stationary.

Distance vs. Displacement

As we study the motion of objects, we must first be able to describe the object’s position. Before your parent drives you to school, the car is sitting in your driveway. Your driveway is the starting position for the car. When you reach your high school, the car has changed position. Its new position is your school.

Physicists use variables to represent terms. We will use d to represent car’s position. We will use a subscript to differentiate between the initial position, d 0 , and the final position, d f . In addition, vectors, which we will discuss later, will be in bold or will have an arrow above the variable. Scalars will be italicized.

Tips For Success

In some books, x or s is used instead of d to describe position. In d 0 , said d naught , the subscript 0 stands for initial . When we begin to talk about two-dimensional motion, sometimes other subscripts will be used to describe horizontal position, d x , or vertical position, d y . So, you might see references to d 0x and d fy .

Now imagine driving from your house to a friend's house located several kilometers away. How far would you drive? The distance an object moves is the length of the path between its initial position and its final position. The distance you drive to your friend's house depends on your path. As shown in Figure 2.5 , distance is different from the length of a straight line between two points. The distance you drive to your friend's house is probably longer than the straight line between the two houses.

We often want to be more precise when we talk about position. The description of an object’s motion often includes more than just the distance it moves. For instance, if it is a five kilometer drive to school, the distance traveled is 5 kilometers. After dropping you off at school and driving back home, your parent will have traveled a total distance of 10 kilometers. The car and your parent will end up in the same starting position in space. The net change in position of an object is its displacement , or Δ d . Δ d . The Greek letter delta, Δ Δ , means change in .

Teacher Demonstration

Help students learn the difference between distance and displacement by showing examples of motion.

As students watch, walk straight across the room and have students estimate the length of your path.
Then, at same starting point, walk along a winding path to the same ending point.
Again, have students estimate the length of your path.

Ask—Which motion showed displacement? Which showed distance? Point out that the first motion shows displacement, and the second shows distance along a path. In both cases, the starting and ending points were the same.

[OL] Be careful that students do not assume that initial position is always zero. Emphasize that although initial position is often zero, motion can start from any position relative to a starting point.

[Visual] Demonstrate positive and negative displacement by placing two meter sticks on the ground with their zero marks end-to-end. As students watch, place a small car at the zero mark. Slowly move the car to students' right a short distance and ask students what its displacement is. Then move the car to the left of the zero mark. Point out that the car now has a negative displacement.

Students will learn more about vectors and scalars later when they study two-dimensional motion. For now, it is sufficient to introduce the terms and let students know that a vector includes information about direction.

[BL] Ask students whether each of the following is a vector quantity or a scalar quantity: temperature (scalar), force (vector), mass (scalar).

[OL] Ask students to provide examples of vector quantities and scalar quantities.

[Kinesthetic] Provide students with large arrows cut from construction paper. Have them use the arrows to identify the magnitude (number or length of arrows) and direction of displacement. Emphasize that distance cannot be represented by arrows because distance does not include direction.

In this activity you will compare distance and displacement. Which term is more useful when making measurements?

1 recorded song available on a portable device
1 tape measure
3 pieces of masking tape
A room (like a gym) with a wall that is large and clear enough for all pairs of students to walk back and forth without running into each other.
One student from each pair should stand with their back to the longest wall in the classroom. Students should stand at least 0.5 meters away from each other. Mark this starting point with a piece of masking tape.
The second student from each pair should stand facing their partner, about two to three meters away. Mark this point with a second piece of masking tape.
Student pairs line up at the starting point along the wall.
The teacher turns on the music. Each pair walks back and forth from the wall to the second marked point until the music stops playing. Keep count of the number of times you walk across the floor.
When the music stops, mark your ending position with the third piece of masking tape.
Measure from your starting, initial position to your ending, final position.
Measure the length of your path from the starting position to the second marked position. Multiply this measurement by the total number of times you walked across the floor. Then add this number to your measurement from step 6.
Compare the two measurements from steps 6 and 7.
Which measurement is your total distance traveled?
Which measurement is your displacement?
When might you want to use one over the other?
Measurement of the total length of your path from the starting position to the final position gives the distance traveled, and the measurement from your initial position to your final position is the displacement. Use distance to describe the total path between starting and ending points,and use displacement to describe the shortest path between starting and ending points.
Measurement of the total length of your path from the starting position to the final position is distance traveled, and the measurement from your initial position to your final position is displacement. Use distance to describe the shortest path between starting and ending points, and use displacement to describe the total path between starting and ending points.
Measurement from your initial position to your final position is distance traveled, and the measurement of the total length of your path from the starting position to the final position is displacement. Use distance to describe the total path between starting and ending points, and use displacement to describe the shortest path between starting and ending points.
Measurement from your initial position to your final position is distance traveled, and the measurement of the total length of your path from the starting position to the final position is displacement. Use distance to describe the shortest path between starting and ending points, and use displacement to describe the total path between starting and ending points.

Choose a room that is large enough for all students to walk unobstructed. Make sure the total path traveled is short enough that students can walk back and forth across it multiple times during the course of a song. Have them measure the distance between the two points and come to a consensus. When students measure their displacement, make sure that they measure forward from the direction they marked as the starting position. After they have completed the lab, have them discuss their results.

If you are describing only your drive to school and the route is a straight line, then the distance traveled and the displacement are the same—5 kilometers. When you are describing the entire round trip, distance and displacement are different. When you describe distance, you only include the magnitude , the size or amount, of the distance traveled. However, when you describe the displacement, you take into account both the magnitude of the change in position and the direction of movement.

In our previous example, the car travels a total of 10 kilometers, but it drives five of those kilometers forward toward school and five of those kilometers back in the opposite direction. If we ascribe the forward direction a positive (+) and the opposite direction a negative (–), then the two quantities will cancel each other out when added together.

A quantity, such as distance, that has magnitude (i.e., how big or how much) and sometimes a sign (e.g., electric charge, temperature in Celsius, or component of a vector) but does not take into account direction is called a scalar . A quantity, such as displacement, that has both magnitude and direction is called a vector . A vector with magnitude zero is a special case of a vector that has no direction.

Watch Physics

Vectors & scalars.

This video introduces and differentiates between vectors and scalars. It also introduces quantities that we will be working with during the study of kinematics.

It explains that distance is a vector and direction is important, whereas displacement is a scalar and it has no direction attached to it.
It explains that distance is a scalar and direction is important, whereas displacement is a vector and it has no direction attached to it.
It explains that distance is a scalar and it has no direction attached to it, whereas displacement is a vector and direction is important.
It explains that both distance and displacement are scalar and no directions are attached to them.

Define the concepts of vectors and scalars before watching the video.

[OL] [BL] Come up with some examples of vectors and scalars and have the students classify each.

[AL] Discuss how the concept of direction might be important for the study of motion.

Displacement Problems

Hopefully you now understand the conceptual difference between distance and displacement. Understanding concepts is half the battle in physics. The other half is math. A stumbling block to new physics students is trying to wade through the math of physics while also trying to understand the associated concepts. This struggle may lead to misconceptions and answers that make no sense. Once the concept is mastered, the math is far less confusing.

So let’s review and see if we can make sense of displacement in terms of numbers and equations. You can calculate an object's displacement by subtracting its original position, d 0 , from its final position d f . In math terms that means

If the final position is the same as the initial position, then Δ d = 0 Δ d = 0 .

To assign numbers and/or direction to these quantities, we need to define an axis with a positive and a negative direction. We also need to define an origin, or O . In Figure 2.6 , the axis is in a straight line with home at zero and school in the positive direction. If we left home and drove the opposite way from school, motion would have been in the negative direction. We would have assigned it a negative value. In the round-trip drive, d f and d 0 were both at zero kilometers. In the one way trip to school, d f was at 5 kilometers and d 0 was at zero km. So, Δ d Δ d was 5 kilometers.

You may place your origin wherever you would like. You have to make sure that you calculate all distances consistently from your zero and you define one direction as positive and the other as negative. Therefore, it makes sense to choose the easiest axis, direction, and zero. In the example above, we took home to be zero because it allowed us to avoid having to interpret a solution with a negative sign.

Worked Example

Calculating distance and displacement.

A cyclist rides 3 km west and then turns around and rides 2 km east. (a) What is her displacement? (b) What distance does she ride? (c) What is the magnitude of her displacement?

To solve this problem, we need to find the difference between the final position and the initial position while taking care to note the direction on the axis. The final position is the sum of the two displacements, Δ d 1 Δ d 1 and Δ d 2 Δ d 2 .

Displacement: The rider’s displacement is Δ d = d f − d 0 = − 1 km Δ d = d f − d 0 = − 1 km .
Distance: The distance traveled is 3 km + 2 km = 5 km.
The magnitude of the displacement is 1 km.

The displacement is negative because we chose east to be positive and west to be negative. We could also have described the displacement as 1 km west. When calculating displacement, the direction mattered, but when calculating distance, the direction did not matter. The problem would work the same way if the problem were in the north–south or y -direction.

Physicists like to use standard units so it is easier to compare notes. The standard units for calculations are called SI units (International System of Units). SI units are based on the metric system. The SI unit for displacement is the meter (m), but sometimes you will see a problem with kilometers, miles, feet, or other units of length. If one unit in a problem is an SI unit and another is not, you will need to convert all of your quantities to the same system before you can carry out the calculation.

Point out to students that the distance for each segment is the absolute value of the displacement along a straight path.

Practice Problems

On an axis in which moving from right to left is positive, what is the displacement and distance of a student who walks 32 m to the right and then 17 m to the left?

Displacement is -15 m and distance is -49 m .
Displacement is -15 m and distance is 49 m.
Displacement is 15 m and distance is -49 m.
Displacement is 15 m and distance is 49 m.

Tiana jogs 1.5 km along a straight path and then turns and jogs 2.4 km in the opposite direction. She then turns back and jogs 0.7 km in the original direction. Let Tiana’s original direction be the positive direction. What are the displacement and distance she jogged?

Displacement is 4.6 km,and distance is -0.2 km.
Displacement is -0.2 km, and distance is 4.6 km.
Displacement is 4.6 km, and distance is +0.2 km.
Displacement is +0.2 km, and distance is 4.6 km.

Work In Physics

Mars probe explosion.

Physicists make calculations all the time, but they do not always get the right answers. In 1998, NASA, the National Aeronautics and Space Administration, launched the Mars Climate Orbiter, shown in Figure 2.7 , a $125-million-dollar satellite designed to monitor the Martian atmosphere. It was supposed to orbit the planet and take readings from a safe distance. The American scientists made calculations in English units (feet, inches, pounds, etc.) and forgot to convert their answers to the standard metric SI units. This was a very costly mistake. Instead of orbiting the planet as planned, the Mars Climate Orbiter ended up flying into the Martian atmosphere. The probe disintegrated. It was one of the biggest embarrassments in NASA’s history.

The text feature describes a real-life miscalculation made by astronomers at NASA. In this case, the Mars Climate Orbiter’s orbit needed to be calculated precisely because its machinery was designed to withstand only a certain amount of atmospheric pressure. The orbiter had to be close enough to the planet to take measurements and far enough away that it could remain structurally sound. One way to teach this concept would be to pick an orbital distance from Mars and have the students calculate the distance of the path and the height from the surface both in SI units and in English units. Ask why failure to convert might be a problem.

Check Your Understanding

What does it mean when motion is described as relative?

It means that motion of any object is described relative to the motion of Earth.
It means that motion of any object is described relative to the motion of any other object.
It means that motion is independent of the frame of reference.
It means that motion depends on the frame of reference selected.
Yes, we would both view the motion from the same reference point because both of us are at rest in Earth’s frame of reference.
Yes, we would both view the motion from the same reference point because both of us are observing the motion from two points on the same straight line.
No, we would both view the motion from different reference points because motion is viewed from two different points; the reference frames are similar but not the same.
No, we would both view the motion from different reference points because response times may be different; so, the motion observed by both of us would be different.
Distance has both magnitude and direction, while displacement has magnitude but no direction.
Distance has magnitude but no direction, while displacement has both magnitude and direction.
Distance has magnitude but no direction, while displacement has only direction.
There is no difference. Both distance and displacement have magnitude and direction.
The perimeter of the race track is the distance; the shortest distance between the start line and the finish line is the magnitude of displacement.
The perimeter of the race track is the magnitude of displacement; the shortest distance between the start and finish line is the distance.
The perimeter of the race track is both the distance and magnitude of displacement.
The shortest distance between the start and the finish line is the magnitude of the displacement vector.
Because Earth is continuously in motion; an object at rest on Earth will be in motion when viewed from outer space.
Because the position of a moving object can be defined only when there is a fixed reference frame.
Because motion is a relative term; it appears differently when viewed from different reference frames.
Because motion is always described in Earth’s frame of reference; if another frame is used, it has to be specified with each situation.

Use the questions under Check Your Understanding to assess students’ achievement of the section’s learning objectives. If students are struggling with a specific objective, the formative assessment will help direct students to the relevant content.

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Authors: Paul Peter Urone, Roger Hinrichs
Publisher/website: OpenStax
Book title: Physics
Publication date: Mar 26, 2020
Location: Houston, Texas
Book URL: https://openstax.org/books/physics/pages/1-introduction
Section URL: https://openstax.org/books/physics/pages/2-1-relative-motion-distance-and-displacement

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IMAGES

Patent US8375375
PPT
Define What is Loop and what are the Types with Syntax.
12.4 Magnetic Field of a Current Loop
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Student Tutorial: Slope Concepts: Definitions

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Zero trip by BUZIMA COMEDY
What is a Flipper Zero and What Does it Do?
Trip edit (loop)
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ZERO Trip, 제주 녹음이 가득한 삼다수숲 웰니스 여행
Flipper Zero : Everyday carry UART serial terminal testing ESP module #flipperzero #gpio

COMMENTS

LLVM Loop Terminology (and Canonical Forms)
This loop definition has some noteworthy consequences: A node can be the header of at most one loop. As such, a loop can be identified by its header. ... (also see Rotated Loops), loop trip count is not the best measure of a loop's number of iterations. For instance, the number of header executions of the code below for a non-positive n ...
zero-trip loop
A Dictionary of Computing. Chymotrypsinogen. zero-trip loop See do-while loop. Source for information on zero-trip loop: A Dictionary of Computing dictionary.
Möbius strip
A Möbius strip made with paper and adhesive tape In mathematics, a Möbius strip, Möbius band, or Möbius loop [a] is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist. As a mathematical object, it was discovered by Johann Benedict Listing and August Ferdinand Möbius in 1858, but it had already appeared in Roman mosaics from the third century ...
Implementing Higher-Order Functions
The Zero-Trip Do Loop The first programming language that provided a level of abstraction over the instructions understood directly by computer hardware was Fortran, a language that is still widely used today despite the advances in programming language design since then.
PDF Generalizing Parametric Timing Analysis
of the inner loop being zero-trip or partially zero-trip. A zero-trip loop derives its name from the fact that a summation whose lower bound exceeds its upper bound evaluates to zero. Hence, a zero-trip loop does not execute the loop body. A partially zero-trip loop fails to execute the loop body on some iterations. If the condition of the ...
10.4: Kirchhoff's Rules
Kirchhoff's Rules. Kirchhoff's first rule—the junction rule. The sum of all currents entering a junction must equal the sum of all currents leaving the junction: ∑Iin = ∑Iout. Kirchhoff's second rule—the loop rule. The algebraic sum of changes in potential around any closed circuit path (loop) must be zero: ∑V = 0.
21.3: Kirchhoff's Rules
Definition: Kirchhoff's Rules. Kirchhoff's first rule—the junction rule: The sum of all currents entering a junction must equal the sum of all currents leaving the junction. Kirchhoff's second rule—the loop rule: The algebraic sum of changes in potential around any closed circuit path (loop) must be zero.
Loop Rule
The Loop Rule, also known as Kirchhoff's Second Law, is a fundamental principle of electric circuits which states that the sum of potential differences around a closed circuit is equal to zero. More simply, when you travel around an entire circuit loop, you will return to the starting voltage. Note that is only true when the magnetic field is ...
PDF Performance Analysis of Symbolic Analysis Techniques for Parallelizing
whether a certain loop is a zero-trip loop for induction variable substitution, and to solve data dependence problems that involve symbolic loop bounds and array subscripts. Range Propagation [3] is the basis for this functionality. It can determine the value ranges that symbolic expressions in the program can as-sume.
Zero-trip loop
Archaeology; Art & Architecture ; Bilingual dictionaries ; Classical studies; Encyclopedias. Geographical reference; English Dictionaries and Thesauri ; History
Basics of Trips, Interlocks, Permissives & Sequences
The Trip must be 'reset' by the operator before the pump can be re-started. The Trip can only be 'reset' if the level in the tank has fallen to a safe level. Resetting the Trip will not cause the pump to automatically re-start, however it may be re-started by an operator action or a control system command e.g. part of a sequence.
Kirchhoff's Voltage Law and the Conservation of Energy
Kirchhoff's voltage law states that the algebraic sum of the potential differences in any loop must be equal to zero as: ΣV = 0. Since the two resistors, R1 and R2 are wired together in a series connection, they are both part of the same loop so the same current must flow through each resistor. Thus the voltage drop across resistor, R 1 = I ...
Loop-the-loop
Loop-the-loop. A loop-the-loop track consists of an incline that leads into a circular loop of radius r. ... Step 1: Define/draw diagram and coordinate system. Step 2: Choose a consistent zero. Step 3: Energy conservation. Step 4: Losses. Step 2: The zero level for potential energy is the bottom of the loop. Step 3: U i + K i = U f + K f. K i ...
Kirchhoff's Loop Rule Formula: Definition, Equations and Examples
Definition. Kirchhoff's loop rule explains that the sum of all the electric potential differences nearby a loop is 0. Sometimes, we also refer to it as Kirchhoff's voltage law or Kirchhoff's second law. In other words, it states that the energy which the battery supplies get used up by all the other components in a loop.
Recursion
Recursion occurs when the definition of a concept or process depends on a simpler or previous version of ... "Zero is a natural number, and each natural number has a successor, which is also a natural number." By this base case and recursive rule, one can generate the set ... this immediately creates the possibility of an endless loop ...
Zero-trip loop
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Kirchhoff's loop rule review (article)
Kirchhoff's loop rule. Kirchhoff's loop rule states that the sum of all the electric potential differences around a loop is zero. It is also sometimes called Kirchhoff's voltage law or Kirchhoff's second law. This means that the energy supplied by the battery is used up by all the other components in a loop, since energy can't enter ...
2.1 Relative Motion, Distance, and Displacement
To assign numbers and/or direction to these quantities, we need to define an axis with a positive and a negative direction. We also need to define an origin, or O. In Figure 2.6, the axis is in a straight line with home at zero and school in the positive direction. If we left home and drove the opposite way from school, motion would have been ...
Zero trip R for loop
r. loops. asked Jul 15, 2021 at 18:58. Fortranner. 2,585 2 23 28. 1. R, for some arcane design reason, decides that 1:0 creates a sequence counting down. You need to use seq_along to generate what you want. Also apparently don't use seq alone, because that one is broken.
What is Zero Sequence Current? Definition & Explanation
Zero Sequence Current. Definition: The unbalanced current flows in the circuit during the earth fault is known as the zero sequence current or the DC component of the fault current.The zero phase sequence means the magnitude of three phases has zero phase displacement.The three vector lines represent the zero sequence current and it is detected ...
define zero trip loop
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Meaning of Zero-Trip Loop in Serbian
Definition of Zero-Trip Loop in English to Serbian language dictionary. World of Dictionary. Open menu. ... Zero-Trip Loop. Zero-Trip Loop Nulta, Petlja. Near entries. Zero Hour Zero Mark Zero Matrix Zero Suppression Zero Value Zero Word Zero-Trip Loop Zest Zidarski Radov Zidarski Zanat. Related entries.
Zero-G Pure Trip Hop Download
Pure Trip from Zero-G features ingredients for constructing accomplished trip hop, including 30 musical pieces divided into their separate elements plus extra helpings of beat loop samples, bass lines, EP chords and drum hits. It's difficult to define trip-hop, and most trip-hop artists deny they are part of any scene at all.