A LevelMathsAQAMechanicsRevision NotesMomentsMomentsUsing Moments with Equilibrium

Using Moments with Equilibrium (AQA A Level Maths: Mechanics): Revision Note

Exam code: 7357

Written by: Dan Finlay

Reviewed by: Lucy Kirkham

Updated on 2 July 2026

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Using moments with equilibrium

What is the resultant moment for a body in equilibrium?

If a rigid body is in equilibrium then:
- The resultant force is 0 N
- The resultant moment about any point is 0 N m
The sum of the magnitudes of the clockwise moments equals the sum of the magnitudes of the anti-clockwise moments

How do I use F = ma and moments to solve equilibrium problems?

Step 1: Identify all forces and perpendicular distances from the pivot
Step 2: Use the fact that the resultant force is 0 N to form an equation
Step 3: Use the fact that the resultant moment about any point is 0 N m to form equations
- If there is an unknown force you can choose a pivot that is on the line of action of that force – this will mean that the moment of that force is 0 N m
Step 4: Solve the equations

Worked Example

A light rod AB of length 10 m is held in equilibrium by three forces: 50 N, T₁ N and T₂ N.

T₁ N acts vertically upwards at A, 50 N acts vertically downwards 6 m away from A and T₂ N acts vertically upwards 2 m away from B as shown in the diagram.

Diagram of a horizontal beam AB, with supports at A and B. Loads: 50 N downward at midpoint, T1 N upward at A, T2 N upward at B, with distances given.

Find the values of T₁ and T₂.

Answer:

4-1-2-using-moments---equilibrium-example-solution

Examiner Tips and Tricks

If you see a force diagram that involves distances then you can be fairly sure that moments will be involved! A clear diagram showing all the distances is key.
If you pick a pivot and form a moment equation which involves more than one unknown, try choosing another pivot to form simultaneous equations.
Pick your pivot wisely as unknown and unwanted forces can be eliminated from the equation by choosing the point to be on the line of action of a force.

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