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Equilibrium and the principle of moments Cambridge International AS & A Level Physics revision

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In plain words

For something to stay completely still, two things must be true: the forces on it balance, so it doesn't start to move, and their turning effects balance, so it doesn't start to spin. Use both and you can find any unknown force on a bridge, a shelf or a see-saw.

Three things to know

  1. Principle of moments: for a body in equilibrium, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about that point.
  2. A body is in equilibrium when there is no resultant force on it and no resultant moment (torque).
  3. Three coplanar forces in equilibrium form a closed triangle when drawn tip to tail.

Worked example

A uniform plank 3.0 m long weighing 120 N rests on supports at its ends, A and B. A 600 N person stands 1.0 m from A. Find the force at each support.

  1. Take moments about A, so the force at A doesn't appear: R_B × 3.0 = 120 × 1.5 + 600 × 1.0 = 780 N m.
  2. R_B = 260 N.
  3. Vertically the forces balance: R_A + 260 = 720, so R_A = 460 N.

Tips and tricks

  • Take moments about a point where an unknown force acts. That force then has no moment and drops out.
  • Then use "forces up = forces down" to find the other unknown.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Equilibrium and the principle of moments: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. A see-saw balances with a 400 N child 1.5 m from the pivot. How far from the pivot is the 600 N child on the other side?
    • 0.67 m
    • 1.0 m (the answer)
    • 1.5 m
    • 2.25 m

    400 × 1.5 = 600 × d.

  2. A body has zero resultant force but a non-zero resultant moment. What does it do?
    • stays at rest
    • moves off in a straight line
    • starts to rotate (the answer)
    • nothing

    Both conditions are needed for equilibrium.

  3. A uniform beam rests on a support at each end, A and B. A load is placed nearer to A. Which support pushes up with the larger force?
    • A (the answer)
    • B
    • they push equally
    • neither pushes

    The nearer support takes more of the load.

  4. About which point can moments be taken for a body in equilibrium?
    • any point (the answer)
    • only the centre of gravity
    • only the pivot
    • only one end

    The moments balance about every point.

  5. A uniform metre rule balances on a pivot at the 40 cm mark when a 2.0 N weight hangs from the 10 cm mark. What is the weight of the rule?
    • 0.67 N
    • 2.0 N
    • 6.0 N (the answer)
    • 8.0 N

    2.0 × 0.30 = W × 0.10, since the rule's weight acts at the 50 cm mark.

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