Moment of a force

What is a moment of force?

A measure of the turning effect produced by the force about an axis.

The magnitude of the moments is the product of the forces and the perpendicular distance from point about which the moment is considered, to the line of action of the force.

The Principle of Moments

The Principle of Moments can be summarized as follows:

In order for an object to achieve rotational equilibrium, the total sum of all the moments of the forces acting upon it around any given axis must be zero.

In other words, the cumulative value of the moments in a clockwise direction is equivalent to the combined value of the moments in an anti-clockwise direction.

Application of Moments

• Longer spanner would be more effective than a shorter spanner because it will produce a greater moment.
• A screw driver which has a thicker handle or a wider handle produces a greater moment than one with a smaller/narrower handle.

Example (1)

• A uniform plank of weight 200N is pivoted at its center of gravity. The plank is 2m in length. A 50N force is placed 10cm from one end.
• Determine the force, F which must must be placed 40cm from the opposite end so as to maintain balance

SOLUTION:

Total clockwise moment = F × 60 Ncm

= 60 F Ncm

Total anti-clockwise moment = 50 × 90 Ncm

= 4500 Ncm

For rotational equilibrium

Total clockwise moment = Total anti-clockwise moment

∴ 60F = 4500

F = 4500/60

F = 75N

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Christopher Seebaran (pc)

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