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Physics · Grades 8–11

Moments, pivots and equilibrium

Use perpendicular distances and check both force and turning balance.

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Learn the idea

Moment

The turning effect about a pivot is force times perpendicular distance from the pivot to the force line.

Rotational balance

For equilibrium, clockwise and anticlockwise moments balance.

Translational balance

A balanced moment total does not by itself prove zero net force.

Model assumptions

A weightless beam is an idealization. A real beam's weight can add its own moment.

Worked examples

A 10 N perpendicular force acts 0.4 m from a pivot. Find its moment magnitude.

10 × 0.4 = 4 N·m.

4 N·m

A 12 N force acts 2 m left of a pivot. What downward force 3 m right balances it on a weightless beam?

12 × 2 = F × 3, so F = 8 N.

8 N

Check your understanding

  1. Which distance belongs in a moment calculation?

    1. Always the entire beam length
    2. Any distance drawn on the page
    3. Perpendicular distance to the force line

  2. A 15 N force has a 6 N·m moment. Find perpendicular lever arm.

  3. Why can ignoring a heavy beam's weight change a balance calculation?

Answers and marking notes

Answers and marking notes
  1. Perpendicular distance to the force line

    The lever arm is measured perpendicular to the force line.

  2. 0.4 m

    d = moment/force = 6/15 = 0.4 m.

  3. The beam's weight may have a moment about the pivot.

    Credit the beam's centre of mass or its force line.

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.

Independent educational review required. Grade bands are approximate; these are not officially aligned curricula.