All subjects · Mathematics · WME01 (M1)

Moments of forces

A force can make a body turn. The turning effect about a point is its moment. For a rigid body in equilibrium, the moments must balance as well as the forces.

Moment of a force

Moment = force × perpendicular distance from the point to the line of action of the force. The unit is N m. State whether it is clockwise or anticlockwise.

Two conditions

A rigid body is in equilibrium when:

1. the resultant force is zero, and

2. the sum of the moments about any point is zero (clockwise = anticlockwise).

In M1 the forces are parallel, so condition 1 is just: total up = total down.

Taking moments

Take moments about a point where an unknown force acts: that force has zero moment there and drops out of the equation. Write the equation in a clear form such as "M(A): 40 × 1.5 = R × 2".

Worked example

A child of mass 30 kg sits 1.5 m from the pivot of a light seesaw. Where must a child of mass 25 kg sit to balance it?

  1. Moments about the pivot: 30g × 1.5 = 25g × d.
  2. g cancels: 45 = 25d.

Answer: d = 1.8 m from the pivot, on the other side

Key idea: Moment = F × perpendicular distance. Equilibrium: forces balance and moments balance about any point. Take moments where an unknown acts.

Check yourself

  1. Find the moment of a 12 N force about a point 0.5 m from its line of action.
    Show answer

    6 N m. 12 × 0.5 = 6 N m.

  2. A light rod is pivoted at its centre. A 40 N weight hangs 1.2 m to the left of the pivot. How far to the right must a 30 N weight hang for balance?
    Show answer

    1.6 m. 40 × 1.2 = 30d, so d = 1.6 m.

  3. A light rod AB of length 4 m has downward forces of 10 N at A, 15 N at 1 m from A, and 20 N at B. With A at the left-hand end, find the total clockwise moment about A.
    Show answer

    95 N m. 15 × 1 + 20 × 4 = 95 N m (the force at A has no moment about A).

  4. A light rod rests in equilibrium on a pivot. A 25 kg mass hangs 0.8 m to the left of the pivot and a 20 kg mass hangs 1 m to the right. Find the reaction at the pivot, to 3 significant figures.
    Show answer

    441 N. Moments balance (25g × 0.8 = 20g × 1), and vertically the pivot holds up the total weight: R = 45g = 441 N.

  5. A 70 N force has a moment of 84 N m about a point P. Find the perpendicular distance from P to its line of action.
    Show answer

    1.2 m. d = 84/70 = 1.2 m.

  6. When taking moments to find the reaction at support B, which point is usually best to take moments about?
    • Support B
    • The midpoint of the rod, always
    • The other support, A
    • The end with the heaviest load
    Show answer

    The other support, A. Taking moments about A removes the unknown reaction at A, leaving R_B as the only unknown.

  7. What is the unit of a moment?
    • N m
    • N/m
    • N s
    • kg m
    Show answer

    N m. Force (N) × distance (m).

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Last updated 7 November 2026. Spotted a mistake? Tell us.