Turning effects of forces

AS Level Physics · Forces, density and pressure. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.

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The idea

The moment of a force measures its turning effect about a point. It depends on the size of the force and on the perpendicular distance from the point to the line of action of the force. If the force is not at right angles to the lever, use only the perpendicular distance (or the perpendicular component of the force).

The weight of an object can be taken to act at a single point, its centre of gravity. For a uniform beam this is at the middle.

A couple is a pair of equal and opposite forces whose lines of action do not coincide. Its resultant force is zero, so it produces rotation only. Its turning effect is called a torque.

Rules to remember

Common mistake

For a couple, students multiply the force by the distance to the centre, which gives half the torque. Use the full perpendicular distance between the two forces, and use one force, not both.

Worked example

Two forces of 8.0 N form a couple. They act in opposite directions at the two ends of a rod 0.30 m long, each at 50° to the rod. What is the torque of the couple? (sin 50° = 0.766)

  1. The forces are not at right angles to the rod, so find the perpendicular distance between their lines of action.
  2. Perpendicular distance = 0.30 × sin 50° = 0.30 × 0.766 = 0.230 m.
  3. Torque = one force × perpendicular distance = 8.0 × 0.230 = 1.84 N m.

Answer: About 1.8 N m.

Practice questions

Try each one, then open the answer.

1. The centre of gravity of an object is

  1. A
    the geometric centre of the object
  2. B
    the point where the whole weight of the object may be considered to act
  3. C
    the heaviest point of the object
  4. D
    always inside the object
Show answer

Answer: B. It is the point through which the resultant gravitational force acts. For a ring it lies outside the material.

2. A couple consists of

  1. A
    two equal forces acting in the same direction along the same line
  2. B
    two equal and opposite forces whose lines of action do not coincide, producing rotation only
  3. C
    a force and its reaction
  4. D
    two forces at right angles
Show answer

Answer: B. A couple gives a turning effect (torque = one force × perpendicular separation) with no resultant force.

3. A door is opened by a force of 25 N applied at right angles to the door, 0.80 m from the hinge. What force, applied at right angles 0.50 m from the hinge, gives the same moment?

  1. A
    16 N
  2. B
    25 N
  3. C
    40 N
  4. D
    50 N
Show answer

Answer: C. Moment = 25 × 0.80 = 20 N m. At 0.50 m: F = 20 ÷ 0.50 = 40 N. A smaller distance needs a larger force.

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