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    Moments and the principle of moments

    By Engr. Mehmood Kakar · Updated

    Quick answer

    A moment is the turning effect of a force: moment = force × perpendicular distance from the pivot (M = Fd), in N m. If an object is balanced, the total clockwise moment about the pivot equals the total anticlockwise moment. Use that to find an unknown force or distance.

    What a moment is

    Push a door near the hinge and it barely moves. Push the same amount near the handle and it swings open. The turning effect of a force, its moment, depends on the force and on how far from the pivot it acts:

    moment (N m) = force (N) × perpendicular distance from the pivot (m)

    A 30 N force is applied 0.5 m from the hinge of a door, at right angles to the door. Calculate the moment. (2 marks)

    1. M = F × d
    2. M = 30 × 0.5
    3. M = 15 N m

    The principle of moments

    When an object is balanced, the turning effects on each side cancel out:

    total clockwise moment = total anticlockwise moment

    Every balance question uses this one idea. Work out the moment on the side where you know everything, then set the other side equal to it.

    Balancing a see-saw

    A child of weight 400 N sits 1.5 m from the pivot of a see-saw. Where must a 500 N child sit on the other side to balance it? (3 marks)

    1. Anticlockwise moment = 400 × 1.5 = 600 N m
    2. Balanced, so clockwise moment = 600 N m
    3. d = 600 ÷ 500
    4. d = 1.2 m from the pivot

    The heavier child sits closer to the pivot. That's a quick check that your answer makes sense.

    Several forces on one side

    If more than one force turns the same way, add their moments.

    A beam is pivoted at its centre. On the right, a 200 N weight hangs 0.6 m from the pivot and a 100 N weight hangs 1.0 m from the pivot. What force, 0.8 m to the left of the pivot, balances the beam? (4 marks)

    1. Clockwise moments: 200 × 0.6 + 100 × 1.0 = 120 + 100 = 220 N m
    2. Anticlockwise moment must also be 220 N m
    3. F = 220 ÷ 0.8
    4. F = 275 N

    Levers

    A lever is a force multiplier. A small effort far from the pivot can balance a large load close to it.

    A crowbar is used to lift a rock. The pivot is 0.2 m from the rock and the effort of 100 N is applied 1.2 m from the pivot. What force does the crowbar exert on the rock? (3 marks)

    1. Moment of effort = 100 × 1.2 = 120 N m
    2. Same moment on the rock side: F × 0.2 = 120
    3. F = 120 ÷ 0.2 = 600 N

    The 100 N effort becomes a 600 N force on the rock, because the effort is six times further from the pivot.

    Gears

    Gears pass a turning effect from one shaft to another. When a small gear drives a larger one, the larger gear turns more slowly but with a bigger moment, because its teeth are further from its centre. When a large gear drives a smaller one, the smaller gear turns faster with a smaller moment. Bicycle gears use this: a low gear makes pedalling uphill easier.

    Practice

    1. A 50 N force acts 0.3 m from a pivot. Calculate the moment.

    M = 50 × 0.3 → M = 15 N m

    2. A 600 N adult sits 1.0 m from the pivot of a see-saw. Where must a 300 N child sit to balance?

    Adult’s moment = 600 × 1.0 = 600 N m → d = 600 ÷ 300 = 2.0 m

    3. A wheelbarrow carries a 400 N load 0.5 m from the wheel (the pivot). The handles are 1.6 m from the wheel. What upward force is needed at the handles?

    Load moment = 400 × 0.5 = 200 N m → F = 200 ÷ 1.6 = 125 N

    Frequently asked questions

    What is the unit of a moment?

    The newton-metre (N m). If distances are given in centimetres you can work in N cm, as long as both sides use the same unit.

    What is the principle of moments?

    For an object that is balanced, the sum of the clockwise moments about a pivot equals the sum of the anticlockwise moments about the same pivot.

    How do levers make jobs easier?

    A lever lets a small effort, applied far from the pivot, create the same moment as a large load close to the pivot. The lever acts as a force multiplier.

    Are moments in Combined Science?

    In AQA, moments, levers and gears are in GCSE Physics (separate science) only.

    Engr. Mehmood Kakar

    Written by Engr. Mehmood Kakar

    Physics educator and engineer (MSc Physics, B.Ed, M.Ed) with 8 years of hands-on teaching, from college students to teacher training. About the author · LinkedIn (opens in a new tab)

    Checked against the AQA GCSE Physics (8463) specification on 14 November 2026.