Moments

Overview

Moments describe the turning effect of a force. In this lesson you connect force, perpendicular distance, centre of gravity, and couples so that rotation problems become a clear choice of pivot and equation.

What You Need to Know

• The moment of a force is force x perpendicular distance from the pivot.
• The line of action matters. Use the shortest perpendicular distance from the pivot to the force.
• Weight can usually be treated as acting at the centre of gravity.
• A couple is two equal and opposite forces whose lines of action are different, so the effect is rotation only.
• The torque of a couple is one force multiplied by the perpendicular distance between the two lines of action.

How to Work Through It

1. Start by labelling forces, pivots, and perpendicular distances on simple beam diagrams.
2. Calculate individual moments and decide whether each one is clockwise or anticlockwise.
3. Use centre of gravity to model the weight of an object in a turning problem.
4. Compare a single force producing a moment with a couple producing pure rotation.

Check Your Understanding

• Why must the distance in a moment calculation be perpendicular to the force?
• Where would you draw the weight of a uniform ruler?
• How is a couple different from two forces that simply cancel?
• What distance is used when calculating the torque of a couple?

Common Mistakes

• Using the length of an object instead of the perpendicular distance to the line of action.
• Forgetting to state whether a moment is clockwise or anticlockwise.
• Treating a couple as if its two forces produce no turning effect.

Next Steps

• Practise drawing force diagrams before calculating.
• Keep the moment and torque equations ready for equilibrium problems.