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Moments and equilibrium for OCR A-level Physics

Moments and equilibrium

This page covers the following topics:

1. Moments
2. Moments of couples
3. Centre of mass

A moment of a force is the turning effect the forces cause about a fixed point, called the pivot. Moment is measured in Nm and is a vector. The moment of a force may cause a clockwise or an anticlockwise rotation and the direction can be determined using corkscrew rule. The principle of moments states that for an object to be in equilibrium, the total clockwise moment must be equal to the total anticlockwise moment about any pivot on the object.

A lever is defined as a system consisting of a pivot, effort and a load. Gears are wheels with toothed edges that rotate on a shaft, with the teeth of one gear fitted into the teeth of the other. Since at the point of contact the two gears must be moving in the same direction, the two gears rotate in opposite directions.

Moments

A couple is a special case of moments and is created when two parallel forces of the same magnitude and opposite direction act on an object along different lines, producing a turning effect. The moment of a couple, which is a vector, is called torque and can be found by multiplying the magnitude of the force with the distance perpendicular to the forces.

Moments of couples

The centre of mass of an object is a point at which the weight of the object appears to act. For symmetrical objects, the centre of mass is the point of symmetry. If an object is suspended from its centre of mass, it will balance; if not, it will come to rest with the centre of mass vertically below the point from which it is suspended.

The weight of the object can be represented as a downwards arrow starting from the centre of mass; this is called the line of action of the weight. For an object to be in equilibrium, the line of action of its weight must be inside its base; if not, the object will topple over.

Centre of mass

1

A student is trying to balance a beam on a pivot. She would like for the beam to be in equilibrium on its own, with no external forces acting on it. Where should the student place the pivot? Explain your answer.

The pivot should be placed directly underneath the centre of mass. Since the only force acting on the beam is its own weight, when moments are taken from the pivot, they will be 0, and so the beam will be in equilibrium. The line of action of the weight will lie inside the pivot, therefore the beam will balance.

underneath the centre of mass due to weight lying inside pivot

A student is trying to balance a beam on a pivot. She would like for the beam to be in equilibrium on its own, with no external forces acting on it. Where should the student place the pivot? Explain your answer.

2

A gear of radius 0.75 m is turning with a smaller gear of radius 0.2 m. Given that the moment of the smaller gear is 40 Nm, calculate the moment of the larger gear.

M = F ร— d
40 Nm = F ร— 0.2 m
F = 200 N

The force acting on the two gears is equal.
moment of larger gear = 200 N ร— 0.75 m = 150 Nm

150 Nm

A gear of radius 0.75 m is turning with a smaller gear of radius 0.2 m. Given that the moment of the smaller gear is 40 Nm, calculate the moment of the larger gear.

3

An object is suspended from a point and does not move. What does this say about the point it was suspended from?

The point of suspension has to be the centre of mass of the object or directly above it.

The point of suspension is the centre of mass.

An object is suspended from a point and does not move. What does this say about the point it was suspended from?

4

What are the conditions for two forces acting on an object to be considered a couple?

The two forces acting on the object must be of the same magnitude, must be acting in opposite direction and must be acting along different lines. This produces a turning effect on the object.

same magnitude, opposite direction, acting along different lines

What are the conditions for two forces acting on an object to be considered a couple?

5

Which one of the objects given in the diagram is the most stable? Explain why.

The most stable object is the second one because it has the largest base and the lowest centre of mass. This makes it more probable for the line of action of its weight to lie inside its base if moved.

second one due to the largest base and the lowest centre of mass

Which one of the objects given in the diagram is the most stable? Explain why.

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