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

Dan Finlay

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Using Moments - Equilibrium

What happens with moments if a rigid body is 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 solve problems involving moments and equilibrium?

  • 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 13 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.

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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Dan Finlay

Author: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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