Moments

A moment is the turning effect of a force. For an object in equilibrium, the forces balance and the moments about any point balance too. This lets you work out the forces on beams, ladders and see-saws.

Key facts

  • Moment = force × perpendicular distance from the pivot.
  • In equilibrium: clockwise moments = anticlockwise moments about any point.
  • Also, total up forces = total down forces.
  • A uniform beam’s weight acts at its middle.

Worked examples

Example 1

A 4 m uniform beam of weight 200 N rests on supports at each end. A 300 N load sits 1 m from the left end. Find the reaction at the right support.

  1. Clockwise: 300 × 1 + 200 × 2 = 700 Nm.
  2. Anticlockwise: R × 4.
  3. 4R = 700 R = 175 N
  4. Left support: 500 − 175 = 325 N.

Answer: 175 N