Forces - 5.4 Moments, Gears and Levers (GCSE Physics AQA)

Moments, Gears and Levers

Forces and Rotation

We can make an object rotate by applying one force or a system of forces to an object. For example, when you push a door, the door will turn on its hinges.

The turning effect of the force causes the object to rotate.

AQA Specification: Students should be able to describe examples in which forces cause rotation.

Examples of Forces Causing Rotation

For AQA exams, we need to know about a few examples of forces causing rotation.

Moments

• The turning effect of a force is called the moment. Moments are used to describe the turning effect of a force. Previously, we mentioned that the turning effect causes the rotation of an object. Now, we can say that moments cause the rotation of an object.
• Moments vary in size. The size of the moment will affect the amount of rotation produced. If a moment is bigger, then the object will experience a lot of rotation. If the moment is small, then the object will experience very little turning force. In the next section, we will discuss how to change the size of a moment.

Calculating Moments

This is the equation for calculating the size of a moment:

Where:

• moment of a force, M, in newton-metres, Nm
• force, F, in newtons, N
• distance, d, is the perpendicular distance from the pivot to the line of action of the force, in metres, m.

When we are calculating the size of a moment, it is very important to remember that the force is always acting at right angles to the distance measured (Fig 2).

Question: What is the moment of a 4N downwards force acting 0.4m from a pivot?

1. Draw a diagram.
To tackle this question, we should start off by drawing a diagram.

2. Look at the formula.
Now that we have a visual representation, we can see that our force is perpendicular to the distance we were given. Now we can use our formula:

M = Fd

3. Substitute in the numbers.
Once we have put the numbers into the equation, we should get our answer.

M = 4 x 0.4

M = 1.6 Nm

Changing the Size of a Moment

• Moments can be increased. We can increase the size of a moment by either increasing the force applied, or increasing the perpendicular distance from the pivot.
• Moments can be decreased. We can decrease the size of a moment by either decreasing the force applied, or decreasing the perpendicular distance from the pivot.

Balancing Moments

Clockwise and Anticlockwise Moments

Since moments cause objects to rotate, we can classify them by their direction. The two terms that we use to describe the direction of a moment are clockwise and anticlockwise, as in Fig 3.

Balancing Moments

In certain situations, moments can balance each other out and the object will stay still (instead of turning). For this to be the case, the total clockwise moment will be equal to the total anticlockwise moment about a pivot.

If the total clockwise moment doesn’t equal the total anti-clockwise moment, the object will rotate:

Calculating Force and Distance from Moments

Previously, we looked at calculating a moment from a force and a distance. Now, we are going to work backwards, using the moment to find the force or distance.

In these situations, we are going to use the fact that the system is balanced. As we mentioned before, in a balanced system, the total clockwise moment will equal the total anticlockwise moment. By using this principle, we are able to form an equation which will help us to solve questions:

Question: Sam and Jess are sat at opposite ends of a seesaw. Jess weighs 300N and is sat 3 metres away from the centre of the pivot. Sam weighs 450N. Whilst they are sat in their current positions, the seesaw is balanced. How far away is Sam sat from the centre of the pivot?

1. We need to draw a diagram.
It is very important that we draw a clear diagram to see exactly what is going on. Add in all the values for the weights and distances that we know. We will simply label the distance we are trying to find as ‘d’.

2. Assign directions to the moments.
In this case, we can see from the diagram that the Sam is creating an anticlockwise moment, whereas Jess is creating a clockwise moment.

3. Calculate the moment that we have information for.
In this question, we can calculate Jess’s moment. We can do this by using the equation

M = Fd
M = 300 x 3
M = 900 Nm

4. Remember that anticlockwise moments = clockwise moments.
The seesaw is balanced, so we know that the anticlockwise moments are equal to the clockwise moments.

5. Substitute numbers into the equation.
We have already calculated Jess’s moment, so we just need to put in the missing information for Sam.

We can use this information to help us create a balanced equation:

anticlockwise moment = clockwise moment
Sam’s moment = Jess’s moment
Fd = Fd (Since M = Fd)
450 x d = 300 x 3
450 x d = 900
d = 900 / 450
d = 2m

Therefore, we can say that Sam is sat 2m away from the centre of the pivot.

In this question, we found a distance by using the values of the force and the moment. In other questions, we might be asked to find the force when we are given the distance and the moment.

To do this, we would use the same method as above, but just substitute in the relevant numbers.

Multiple Forces

Question: (continued from previous question)… Sam moves his position on the seesaw, and moves his bag from the ground onto his side of the seesaw. The distance between pivot and Sam is double of the distance between pivot and the bag. The bag weighs 100N and Sam weighs 450 N. Jess has not moved – she is 300N and 3m away from the pivot on the other side. How far is the bag from the pivot? The seesaw is still balanced.

1. We need to draw another diagram.
Draw an updated diagram. The distance from the pivot to the bag can be called d and therefore the distance from the pivot to Sam is 2d.

2. Assign directions to the moments.
In this case, we can see from the diagram that Sam and the bag are creating an anticlockwise moment, whereas Jess is creating a clockwise moment.

3. Calculate the moment that we have information for.
In this question, we can calculate Jess’s moment. We know this is 900 Nm from the previous question.

4. Remember that anticlockwise moments = clockwise moments.
The seesaw is balanced, so we know that the anticlockwise moments are equal to the clockwise moments.

5. Substitute numbers into the equation.
We have already calculated Jess’s moment. We know

anticlockwise moment = clockwise moment

Sam + Bag moment = Jess’s moment = 900
Sam’s moment = 450 x 2d = 900d
Bag’s moment = 100 x d = 100d
Sam + Bag moment = 1000d
1000d = 900
d = 0.9

Therefore, we can say that the bag is 0.9m away from the centre of the pivot, and Sam is 1.8m away.

Levers and Gears

Levers and gears will transmit the rotational effects of forces. In other words, they will reduce the amount of work we have to do when turning objects.

By reducing the amount of work we do when turning the object, we can decrease the force needed to turn the object.

By decreasing the force needed, we are putting in less effort to perform certain tasks.

Levers

• Levers increase the size of moments. Leavers increase the distance of the force from the pivot, increasing the moment.
• Spanners can act as levers. A spanner is an everyday example of a lever. When using spanners, we are employing the principle of moments – spanners are long, helping to increase the distance of a turning force, hence increasing the moment.

• The force and distance of a moment are perpendicular. In Fig 6, we can see that the force applied to the spanner and the distance (or ‘effective length’) are at right angles to each other. Therefore, when the force and the spanner are perpendicular to each other, we achieve the greatest distance and therefore the highest moment possible.
• Increasing the length of the spanner increases the moment. By increasing the length of the spanner, we are increasing the size of the moment. This is because our ‘perpendicular distance’ is effectively the length of the spanner (assuming the force is straight). We already know that increasing the perpendicular distance will increase the size of the moment, so we can do the same thing by making the spanner longer.
• Increasing the length of the spanner decreases the force needed. As well as increasing the moment, a longer spanner will decrease the force needed to act on an object.

If we want to keep the value of ‘M’ the same, we can increase the value of ‘d’, whilst decreasing the value of ‘F’. In terms of using a spanner, this means that we can use a long spanner with a small amount of force to turn a nut.