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AS & A-Level Physics 04 — Equilibrium, Density and Pressure

AS & A-Level Physics 04 — Equilibrium, Density and Pressure

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Independent Deckloop revision aligned with the Cambridge International AS & A Level Physics (9702) syllabus, 2025–2027. Not affiliated with or endorsed by Cambridge International Education. Chapter 4 of 26: Equilibrium, density and pressure. Concepts, worked applications and misconception checks.

Physics EN AS & A-Level
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The Moment of a Force

A force applied to an object can cause it to rotate about a fixed point, known as a pivot or fulcrum. This turning effect is quantified by a physical quantity called the moment of the force. The magnitude of the moment depends on two factors: the magnitude of the applied force and the perpendicular distance from the pivot to the line of action of that force. A larger force or a greater perpendicular distance will produce a larger moment. Moments have a direction, which can be either clockwise or anticlockwise. The standard unit for a moment is the newton-metre (N m), which should not be confused with the joule, the unit of energy.

Key points

  • A moment is the turning effect of a single force about a specific pivot point.
  • Moment = Force ×\times perpendicular distance from the pivot to the line of action of the force.
  • The SI unit of moment is the newton-metre (N m).
  • Moments are specified as either clockwise or anticlockwise.

Worked example

Question

A gardener attempts to pull a heavy roller using a handle of length 1.2 m. They pull with a horizontal force of 150 N. The handle is inclined at 40° to the horizontal ground. Assuming the pivot is where the roller touches the ground, what is the turning moment of the force about the pivot?

Solution

1. The force is 150 N. The distance from the pivot to the point of application is 1.2 m.
2. The force is horizontal. The perpendicular distance from the pivot (on the ground) to this horizontal line of action is the vertical height of the point where the force is applied. This height is given by d=1.2 m×sin⁡(40°)d = 1.2 \text{ m} \times \sin(40°).
3. d=1.2×0.6428=0.7713d = 1.2 \times 0.6428 = 0.7713 m.
4. Moment = Force ×d=150 N×0.7713 m=115.7\times d = 150 \text{ N} \times 0.7713 \text{ m} = 115.7 N m.

The moment of the force is 120 N m (to 2 s.f.).

Common pitfalls

  • Using the distance along the object to where the force is applied, instead of the perpendicular distance from the pivot to the force's line of action. This is a very common error when the force is not applied at 90°.
  • Forgetting to convert distances into SI units (metres) before calculation, for example, leaving them in centimetres.

Prerequisites

  • Understanding where weight acts is often necessary to calculate its moment.
  • Resolving forces into perpendicular components is an alternative method for calculating moments.
Further resources