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Forces - Moments
A see-saw is a good example of how the principles of moments can be utilised.

Forces - Moments

A moment is a turning effect of a force and you come across them every day of your life. For the physics GCSE, you need to know some examples of forces that create turning effects, how the principle of moments can be utilised and how to calculate the magnitude of turning forces and moments.

If an object is fixed in place using a pivot (a shaft or other fixing that is designed to allow movement of the object), then you have the exact situation required for a turning force to arise. When an object is placed on something narrower, the narrow object can act as a pivot too, for example, a plank placed on a brick. Finally the edges or curved parts of objects can act as pivots too - take for example, a fork. Placed with the curved side uppermost, it is stable, however, placed with the curved side on the table, pressing downwards on the prongs will create a turning force that raises the handle.

The pivot is sometimes referred to as the fulcrum, especially in the context of levers.

When a force is applied to a pivoted object, if it is to one side or the other of the pivot, the object will experience a moment. If the magnitude of the moment is sufficient to overcome any frictional forces, then the object will turn around the pivot. The size of the moment depends on the size of the force applied and its perpendicular distance from the pivot. The equation for calculating a moment is simply the force multiplied by the distance. The SI unit of force is the newton; the SI unit for distance is metres, so the SI units for moments will be newton metres.

All pivoted systems obey the principle of moments. This tells us that if a pivoted object is not moving, the sum of the anticlockwise moments is the same as the sum of the clockwise moments. Questions on your exam paper will often ask you to work out the force or the distance that would be needed to balance a specific moment. Answering such questions is just a case of rearranging the equation that represents the principle of moments to isolate the term you are required to work out:

anticlockwise force x anticlockwise distance = clockwise force x clockwise distance

In some parts of the world, the circus is still very popular. Several circus acts utilise the principle of moments. Trapeze artists are one such group of performers. The trapeze is just an object that is fixed in place by a pivot, high in the big top tent. They can change the moment on the trapeze by altering the position of their centre of gravity. Some of the more spectacular trapeze artists even use the principle of moments to reach the trapeze - they use a see-saw! One or more members of the troupe will stand on a platform and the trapeze performer stands on the end of a specially strengthened see-saw. The people on the platform jump down together and land on the end of the see-saw. The moment they create is larger than the one created by the single person on the other end, so the force moves the see-saw. As you know, when a force moves, work is done. This work done transfers the gravitational potential energy of the jumpers into kinetic energy, firing the performer upwards to reach their trapeze. There is lots of physics in operation at a circus.

What is a moment?
A turning effect of a force
The mass of an object at a point
The distance of a mass from a pivot
When a system is in equilibrium
Moments can be used to your advantage when using a lever
What is the formula for the size of a moment?
M = F x d
F = M x d
M = Fd
d = M x F
This is a direct proportionality so if the force is greater, the moment is larger. If the distance is longer, the moment will be larger too. The opposite is true for smaller values of both terms of the equation
What does d in the above equation stand for?
Parallel distance from line of action to the pivot
Perpendicular distance from line of action to the pivot
Distance of the plane
Distance between two masses
This is the shortest distance between the point at which the force is acting and the point around which an object pivots

If an object is not turning, the total clockwise moment, compared to the total anti-clockwise moment about any pivot, must be what?

Clockwise moment is twice as large as anti-clockwise moment
Clockwise moment is three times as large as anti-clockwise moment
Clockwise moment is half as large as anti-clockwise moment
Clockwise moment is exactly equal in magnitude to the anti-clockwise moment
For an object to be at rest on a pivot, all the forces acting on it must be in equilibrium
What is the size of a moment if F = 10 N and d = 125 cm?
10.125 N m
1250 N m
12.5 N m
1.25 N m
Did you remember to convert 125 cm into metres?
A see-saw is balanced on a pivot with two children on it. One child is sitting 1.5 m to the left of the pivot and has a mass of 50 kg. Another child of mass 30 kg is sitting on the right hand side of the pivot. What distance away from the pivot is the child on the right of the pivot?
30 cm
1.5 m
2.5 m
Impossible to say without knowing the length of the see-saw
The key word in the question is balanced so the principle of moments calculation can be applied
What is the force that creates a moment of 10 N m when it is applied 0.25 m from the pivot?
30 N
40 N
50 N
60 N
Rearrangement of the equation for calculating the size of a moment
If the point of application of the force was moved further away from the pivot, what would be the effect on the moment?
The moment would be greater because the distance is greater
The moment would remain the same because the force hasn't changed
The moment would be smaller because it is further away and therefore has less effect on the pivot
More information is needed to be able to answer this question
Changing either (or both) of the force and distance will alter the moment. An example of this would be using a spanner to turn a nut. A longer spanner enables you to apply the force from a greater distance, increasing the moment and magnifying the force that your muscles can apply
A plank of wood is balanced on a pivot. One mass of 10 kg is then placed 1 m to the left of the pivot on the wood. What weight needs to be placed 0.5 m to the right of the pivot for the wood to still be balanced?
10 kg
20 kg
10 N
200 N
Did you spot that the question asked for the weight? The weight of an object is the mass multiplied by the strength of the gravitational field - 10 N/kg is an acceptable approximation for the gravitational field strength at the surface of the Earth
Which of the following is an example of the principle of moments being utilised?
Lifting a book
A rock falling
A crowbar being used to lift a drain cover
A USB stick
The crowbar is being used as a lever. Levers are a favourite of the examiners for testing your knowledge of moments
You can find more about this topic by visiting BBC Bitesize - Moments, levers and gears

Author:  Martin Moore

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