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# Moment Physics

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Forces can make objects move, but they can also make objects spin. When this happens, the force exerts a so-called moment on the object, and it is this moment that makes the object spin. Take a moment to learn about moments!

## Definition of a moment in physics

In daily usage, the word moment often refers to a short period of time, but in physics, there is a very different meaning to the word.

In physics, a moment on an object is the turning effect on that object caused by a force.

If there is a nonzero net moment on an object, the object will rotate around a pivot point. On the other hand, if an object is balanced (i.e. not spinning or spinning at a constant rate), then this means that the net moment on the object is zero. This is a situation in which the clockwise moment on an object exactly cancels the anticlockwise moment acting on it.

## Formula of moment in physics

Suppose we have an object with a clear pivoting point and we put a forceon that object. We draw a line through the contact point of the force and in the same direction as that of the force, and we call the perpendicular distance from the pivoting point to that line. See the figure below for an illustration of the setup.

The red dot is the pivot point of the brown stick, F is the force on the stick, and d is the distance to the line, StudySmarter Originals.

The size of the momenton of the object is then defined as the size of the forcemultiplied by the perpendicular distance:

.

Thus, written down using symbols, this equation becomes

.

This equation for moments is very intuitive. If we exert a larger force on an object, then the moment (i.e. turning effect) increases. If we put the same force on the object but at a larger distance from the pivoting point, then we have more leverage, so the moment increases as well.

## Units of moment

From the formula for the size of the moment, we see that the appropriate units of measuring moments are(newton-metres). A force ofat a perpendicular distance to a pivot ofexerts a moment size of. Oneis the same as one(joule), which is a unit of energy. Thus, moments have the same units as energy. However, moments are clearly a very different thing than energy, so if we denote a moment, we usually write it down in units of. This particular use of units makes it clear to all readers that we are talking about a moment and not a form of energy.

## Sample calculations with moments

Let's first look at some qualitative examples of moments.

Suppose your feet were glued to the floor, and someone tries to knock you over. Would they try and push at your ankles or at your shoulders? Assuming you don't want to fall over, you would want him to push at your ankles because this way he can exert only a small moment on you because of the small distance to the pivot point at your feet, and it is not the force but it is the moment he exerts that will make you turn around your pivot (your feet) and fall.

Similar reasoning to the example above leads to the conclusion that people prefer door handles to be on the opposite side of the door that the hinge is, such that the perpendicular distance to the pivot is large and therefore the force required to open the door is small. Let's now take a look at some quantitative examples of calculations with moments.

Let's go back to the figure above. If we push in the indicated direction at a distance offrom the pivot, then the perpendicular distance will be roughly. If we push with a force ofat this distance in this direction, then we exert a moment of.

Suppose somebody is stuck in an elevator and you need to break down the door to rescue them. The force at which the door breaks is. This is a lot more than you can exert with your muscles, so you get a crowbar which gives you leverage. If the crowbar is as is depicted in the illustration below, how much force do you need to exert on the crowbar in order to break the door?

A crowbar (green) is used to break a door (to the right) by using a wall (to the left) to stabilise its pivot (red dot), and where you exert the force F, StudySmarter Originals.

Well, we see that we need to exert a moment ofon the door, so the force we need to exert on the crowbar is

.

Suddenly, this force is very realistic for a person to exert on an object, and we are able to break the door.

## Experiment with moments in physics

If you have ever been on a seesaw, then you have unconsciously experimented with moments. Let's examine this familiar situation!

Alice and her dad Bob are sitting on a seesaw and want to make it balance. Alice is lazy and does not want to move, so she stays a distance ofaway from the pivot. The mass of Alice isand the mass of Bob is. At what distance from the pivot does Bob need to sit in order for the seesaw to be balanced?

Answer: For a balanced seesaw, the moments on the seesaw have to cancel each other out, so. The force on the seesaw is perpendicular to the horizontally balanced seesaw, so the perpendicular distanceis equal to the distance of the person to the pivot. This means that for a balanced seesaw, we require

.

The factor of the gravitational field strength cancels out (so this problem has the same answer on other planets too!), and we calculate

.

We conclude that Bob needs to sit a distance ofaway from the pivot. This makes sense: Alice needs 4 times as much leverage as Bob to compensate for her weight being 4 times as small as Bob's weight.

If you do not know someone's mass, you can figure it out by combining your knowledge of your own mass with observations of your distances to the pivot of a balanced seesaw. Your friend's mass is given by

.

## Measurement of moment

Let's think about how you would measure the size of a moment. A logical way to go about this is to exert a moment in the other direction and see what moment it takes to cause the object to become balanced or unbalanced. Below is an example to make this process clear.

Suppose you have a spanner and you want to know the size of the moment it takes to undo a certain nut. You get a machine that delivers a constant large force, say, and a string such that you can exert a force on the spanner at a very specific place. See the illustration below for the setup. You then start by placing the string as close to the nut (the middle of which is the pivot) as possible. Chances are the spanner doesn't move, because the distanceis so small that the moment on the spanner is also small. Slowly you move the string further and further away from the nut, thereby exerting a larger and larger moment on the nut through an increasing perpendicular distance of the force to the pivot. At some distanceto the pivot, the nut starts to turn. You record this distanceto be. Then the moment you exerted on the nut was. You conclude that it takes a moment of aboutto undo this particular nut.

A spanner and a nut, with the pivot, string, and the force delivering machine, StudySmarter Originals.

## Moment Physics - Key takeaways

• A moment on an object is the turning effect on that object caused by a force.
• If an object is balanced, then this means that the net moment on that object is zero. The clockwise moments cancel out the anticlockwise moments.
• We draw a line through the contact point of the force and in the same direction as that of the force, and we call the perpendicular distance from the pivoting point to that line.
• A momentby a forceat a perpendicular distanceis given by.
• We measure the size of moments in.
• Typical practical situations in which moments play a large role are crowbars, seesaws, and spanners.

A moment in physics is the turning effect on an object caused by a force. Think of applying a force to a steering wheel or a spanner in order to make things spin: these forces exert moments on the objects in question.

The moment on an object is calculated by multiplying the force on the object by the perpendicular distance of contact point of the force to the object's pivot. It is handy to look at pictures to see what we mean by the term perpendicular distance.

There is a big difference between moment and momentum. The momentum of an object is a measure of the amount of motion the object possesses, while the moment on an object is a measure of the turning effect being exerted on that object.

An example of a moment in physics is the moment you exert when using a spanner: you exert a force at a certain perpendicular distance to the nut, which is the pivot.

The equation describing the moment on an object is M=Fd, where F is the force on the object and d is the perpendicular distance of the contact point of the force to the pivot of the object. It is handy to look at pictures to see what we mean by the term perpendicular distance.

## Final Moment Physics Quiz

Question

What is elastic force?

After being stretched or compressed, the force that permits some materials to recover to their previous form is known as elastic force or spring force.

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Question

Is elastic and spring force the same?

Yes.

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Question

Is the force gained by an elastic object proportional to the external force used to stretch or compress the object?

Yes. The force gained by an elastic object is directly proportional to the external force used to stretch or compress the object.

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Question

After being compressed or stretched, does the elastic force remain in the elastic body ?

After being compressed or stretched, the elastic force will be maintained in the body until it returns to its original shape.

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Question

Stretching, compressing, twisting, and rotating are some of the most common deformations.

Is this statement true or false?

It is true.

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Question

What are the characteristics of an ideal spring?

A massless, frictionless, unbreakable, and indefinitely stretchy spring is considered as an ideal spring

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Question

When an ideal springs are contracted, they pull. When they are stretched, they push.

Is it true or false?

False,

When such springs are contracted, they push.

When they are stretched, they pull.

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Question

What is an elastic potential energy?

The energy held in elastic materials as a result of stretching or compressing is known as elastic potential energy.

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Question

Name one parameter that affects the elastic potential energy stored in a spring:

The quantity of elastic potential energy stored in such a device is proportional to its stretch; the greater the stretch, the more energy is stored.

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Question

If an object attached to a spring is left under its gravitational force, then the elastic force of the soring would be equal to the gravitational force of the object?

Yes. The spring force applied to the mass by the spring is equal to and opposes the force of gravity. Because the spring would be able to return its original form with the same force.

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Question

Are elastic forces conservative?

The elastic force is conservative, since it only depends on the displacement x, and independent on the path taken.

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Question

The greater the stretch, the more energy is stored in the string.

Is it true or false?

True.

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Question

What is the definition of a moment?

The rotational, or turning effect of a force.

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Question

What are the units of moment?

N m.

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Question

In the formula of moment, what does the distance signify?

It is the perpendicular distance from the line of action of a force to pivot.

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Question

Where would the force on a spanner need to be applied for a maximum moment, provided the force is acting perpendicular to the distance from the pivot?

At the end of a spanner.

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Question

What is the moment generated by a spanner if the applied force is 40 N and the perpendicular distance from the force to the center of the nut is 0.4 m?

16 N m.

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Question

What does the principle of moment state?

The principle of moment states that when a system is in equilibrium, the sum of clockwise moments is equal to the sum of anticlockwise moments.

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Question

In which of the following directions can a moment occur?

Clockwise and anticlockwise.

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Question

If the sum of clockwise moments and anticlockwise moments become equal, then what would happen to the object?

The object would be In equilibrium.

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Question

If the resultant moment is not zero, then what can be said about the object?

The object is in not equilibrium.

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Question

In which of the following does the size of a moment depend?

Size of the force and perpendicular distance between the force.

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Question

What is the point called where the seesaw is fixed and it rotates?

Pivot.

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Question

If the applied force at the end of a spanner is at an angle, what can be said about the moment generated?

The moment will be less than the maximum moment value.

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Question

What is a moment?

A moment is the turning effect of a force.

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Question

A force acting directly through the pivot of a system produces no moment. Is this true or false?

True

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Question

What is the principle of moments?

When a system is in equilibrium, the sum of the clockwise moments equals the sum of anticlockwise moments.

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Question

Give an example of when moments are used in everyday life.

For example: spanners, door handles, see-saws etc

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Question

Give an example of a lever.

eg a pair of scissors, a door handle

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Question

Will a larger or smaller gear complete a turn faster?

A smaller gear

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Question

Which of the following is an example of a use of gears

Bicycles

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Question

If two differently sized gears are connected, which one has a greater moment?

The larger gear as the force applied is the same for both, but the radius is greater for the larger one.

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Question

Why is the effort force used to lift a load with a wheelbarrow less than lifting the load without it?

Because the same moment can be applied with less force if the force is applied further away from the pivot.

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Question

What is a pivot?

A fixed point around which a system can rotate.

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Question

A moment of 0.2 Nm needs to be applied to a door handle to be able to open the door. If the length of the door handle is 0.1 m, what force must be applied?

2 N

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Question

A 20 kg child sits on the right-hand side of a see-saw at 1.5m from the centre. At what distance must a 30 kg child sit on the opposite side to balance the see-saw?

1 m

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Question

A person lifts a wheelbarrow by applying a force of 20 N. If the distance of the handlebars from the wheels is 1.5 m, what is the moment?

30 Nm

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Question

What can be said about the moment if the force applied is parallel to the distance from the pivot?

The moment generated would be zero.

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Question

Which of the following are the correct number of states of equilibrium?

3

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