Using Moments with Equilibrium (Edexcel International AS Maths) : Revision Note
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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.
Find the values of T1 and T2.
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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