# Moments

## Key points

• When a force is applied to an object it can cause it to rotate.

• The rotational effect of a force is called a moment.

## What is a moment?

A moment is the turning effect of a force. Forces that create a moment act around a point called the pivot. The pivot is the point around which the object can rotate or turn.

On a seesaw the pivot is the point in the middle.

It makes calculations easier to try to measure the perpendicular distance between the of the force and the pivot.

For example, if you apply a force to a spanner it rotates. The pivot is at the bolt.

When you push open a door, you apply a force to the edge of the door furthest from the hinges.

This force has a turning effect on the door - a moment which causes the door to rotate around the hinges - the - and the door opens.

The size of a depends on two things:

• the size of the force that is applied

• the distance the force acts from the pivot

It is very important to remember that the distance from the pivot is measured at a right angle, or , to the line of action of the force.

## Moments and levers

Watch the video to understand more about moments and levers.

## Calculating a moment

Calculate the size of a moment using the following equation:

$$Moment~of~a~force = force \times perpendicular~distance~from~pivot$$

or

$$M = F \times d$$

where:

• moment (M) is measured in newton metres (Nm)

• force (F) is measured in newtons (N)

• perpendicular distance from pivot (d) is measured in metres (m)

For example:

To open a door, a person pushes on the edge of a door with a force of 20 N. The distance between their hand and the hinges is 0.7 metres. What is the moment used to open the door?

M = ?

F = 20 N

d = 0.7 m

Use the following equation to calculate the size of a moment:

$$M = F \times d$$

Substitute in the values you know:

$$M = 20 \times 0.7$$

$$M = 1.4$$

The moment used to open the door 1.4 Nm.

## Balancing moments

A seesaw is a good example of balancing . If a person sits on one end, the seesaw rotates around the .

However, if a second person sits on the other end, it is possible to balance the seesaw horizontally. This usually requires one person to adjust their distance from the pivot.

The states that for an object to be the total clockwise moment must be equal to the total anti-clockwise moment.

For example:

A seesaw needs to balance. One one side, 3 m from the pivot, is a box which has a weight of 5 N, and on the other is a box which has a weight of 3 N. Calculate the distance needed between the mass which has a weight of 3 N box and the pivot.

Total anti-clockwise moment = total clockwise moment

Step 1: Calculate the clockwise moment using the following equation:

$$M = F \times d$$

M = ?

F = 5 N

D = 3 m

Substitute in the values you know:

$$M = 5 \times 3$$

$$M = 15~Nm$$

The clockwise moment is 15 Nm

Step two - the seesaw needs to be balanced:

Remember - total anti-clockwise moment = total clockwise moment.

We have already calculated that the clockwise moment is 15 Nm.

Use the equation:

$$M = F \times d$$

Substitute in the values you already know:

M = 15 Nm

F = 3 N

d = ?

$$15 = 3 \times d$$

Now divide both sides by 3:

$$\frac{15}{3} = \frac{3 \times d}{3}$$

This cancels to give:

$$5 = d$$

So the distance between the box weighing 3 N and the pivot is 5 metres.

## Using moments

Spanners and levers both use moments.

### Spanners

Spanners are used to turn nuts and bolts. If you need to undo a nut that is very tight, you can:

• use a short spanner and apply a large force

or

• use a long spanner and apply a small force

Using the longer spanner increases the distance from the pivot. This reduces the amount of force needed to undo the nut from the bolt.

### Levers

Removing the lid from a can of paint requires a large lifting force on the lid. A screwdriver acts as a lever.

The pivot is the edge of the can and this is very close to where the strong push is needed to lift the lid to open the can.

A screwdriver with a long handle means that you can push down on the handle of the screwdriver with a small force and still open the can.

## Calculating an upwards force

Have a look at this calculation of an upwards force.

Calculate the upwards force on the lid if the distance from the pivot to the lid is 0.01 m and the horizontal distance from the pivot to the screwdriver handle is 0.15 m. The person is pushing down with a force of 10 N.

Calculate the anticlockwise moment:

F = 10 N

d = 0.15 m

M = ?

$$M = F \times d$$

$$M = 10 \times 0.15$$

Anticlockwise moment = 1.5 Nm

The clockwise moment must be the same:

F = ?

d = 0.01 m

M = 1.5 Nm

$$M = F \times d$$

$$1.5 = F \times 0.01$$

Divide both sides by 0.01:

$$\frac{1.5}{0.01} = {F \times 0.01}{0.01}$$

This cancels to give:

$$150 = F$$

The lifting force on the lid is 150 N.