 1. Moments

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. # 1

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 × d
40 Nm = F × 0.2 m
F = 200 N

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

150 Nm # 2

Calculate the moment of an upwards force of magnitude 70 N at a perpendicular distance of 2.3 m to the left the pivot.

Since the force is acting upwards and is to the left of the pivot, the moment is clockwise.
M = F × d
moment = 70 N × 2.3 m = 161 Nm clockwise

161 Nm clockwise # 3

A wooden beam of length 3 m is placed on a pivot at its centre to form a lever. A force of magnitude 250 N is exerted at one end of the beam. Calculate the greatest load that can be lifted at 0.8 m away from the pivot, on the opposite side of where the force is exerted.

The given force is 1.5 m away from the pivot.
M = F × d
M = 250 N × 1.5 m = 375 Nm
This moment must be equal to the moment of the load.
375 Nm = F × 0.8 m
F = 375 Nm ÷ 0.8 m = 468.75 N

468.75 N # 4

Calculate the moment of a downwards force of magnitude 115 N acting on a lever at a perpendicular distance of 1.8 m to the left the pivot.

Since the force is acting downwards and is to the left of the pivot, the moment is anti-clockwise.
M = F × d
moment = 115 N × 1.8 m = 207 Nm anti-clockwise

207 Nm anti-clockwise # 5

The system presented in the diagram is in equilibrium. Find the value of distance d.

By the principle of moments, 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.

M = F × d
20 N × 4 m + 30 N × 2 m = 45 N × d
d = 3.11 m (3 s. f.)

3.11 m End of page