Moments and equilibrium

Moment of a force

Moment = Fx, where x is the perpendicular distance from the pivot to the line of action of the force. The unit is N m. If the force is at an angle θ to a lever of length d, the moment is F d sin θ.

Principle of moments

For a body in equilibrium, the sum of clockwise moments about any point equals the sum of anticlockwise moments about that point.

Extended bodies in equilibrium

• The resultant force is zero (upward forces = downward forces).
• The resultant moment about any point is zero.
• The weight of the body acts at its centre of gravity (the middle for a uniform beam).

Tip: take moments about a point where an unknown force acts, so that force has no moment and drops out.

Worked example

A uniform 2.0 m plank of weight 100 N rests on supports at each end. A 300 N child stands 0.50 m from the left end. Find the support forces.

1. Moments about the left end: R_right x 2.0 = 100 x 1.0 + 300 x 0.50 = 250
2. R_right = 125 N
3. Forces: R_left = 400 - 125 = 275 N

Answer: 275 N at the left support and 125 N at the right support

Check yourself

1. A force of 25 N acts at a perpendicular distance of 0.40 m from a pivot. Find its moment in N m.
   Show answer

   10 N m. Moment = Fx = 25 x 0.40 = 10 N m.

2. A 40 N weight hangs 0.30 m to the left of a pivot. What force, 0.60 m to the right of the pivot, balances it? Answer in N.
   Show answer

   20 N. 40 x 0.30 = F x 0.60, so F = 20 N.

3. A force of 50 N acts at 60° to a spanner handle, 0.20 m from the nut. Find the moment about the nut in N m, to 3 s.f.
   Show answer

   8.66 N m. Perpendicular component = 50 sin 60° = 43.3 N; moment = 43.3 x 0.20 = 8.66 N m.

4. A uniform metre rule is pivoted at the 30 cm mark. It balances when a 0.50 N weight hangs at the 10 cm mark. Find the weight of the rule in N.
   Show answer

   0.5 N. The rule's weight acts at 50 cm. 0.50 x 0.20 = W x 0.20, so W = 0.50 N.

5. A uniform 4.0 m beam of weight 200 N rests on supports at ends A and B. A 500 N load sits 1.0 m from A. Find the force from support B in N.
   Show answer

   225 N. Moments about A: R_B x 4.0 = 200 x 2.0 + 500 x 1.0 = 900, so R_B = 225 N.

6. Which pair of conditions must both be true for a rigid body to be in equilibrium?
   • Zero resultant force and zero resultant moment
   • Zero resultant force and zero velocity
   • Equal clockwise moments and zero weight
   • Zero resultant moment and constant acceleration
   Show answer

   Zero resultant force and zero resultant moment. Equilibrium needs no linear acceleration and no turning.

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

   N m. Force (N) x distance (m).

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics specification (XPH11/YPH11), Issue 3
• Pearson qualifications: International Advanced Levels Physics (2018)

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