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Lesson: Chapter 11 — Turning Effect of a Force

11.1. Moment of a force 11 of 12

Worked examples

The order of work in a moment problem is always the same: find force × distance on each side, then set the two equal.

Example 1

The problem

A uniform rod AB of length 1 m is suspended at its exact centre and balanced.

  1. A weight of 4 N is now hung at the end B. Find the initial (clockwise) moment it produces.
  2. With that 4 N still at B, what weight hung at a point C, 0.4 m from the centre of the rod, would balance the rod again?

Figure to be added

Figure for example 1 — the 1 m rod AB suspended at its centre, with 4 N at the end B (0.5 m from the centre) and an unknown weight x at C (0.4 m from the centre on the other side).

Solution — part one

The rod hangs from its exact centre, so the distance from the centre to B is 0.5 m.

clockwise moment = force × perpendicular distance

clockwise moment = 4 N × 0.5 m

clockwise moment = 2 N m

Solution — part two

Let the weight hung 0.4 m from the centre be x.

The moment it produces is anticlockwise, and to balance the rod it must equal the moment produced by the 4 N.

x × 0.4 = 4 × 0.5

x × 0.4 = 2

x = 2 ÷ 0.4 = 5 N

Check it: 5 N × 0.4 m = 2 N m, exactly the 2 N m found in part one.

Exercise 11.1 (1)

The problem

A rod AB is 0.8 m long. It is suspended at its exact centre and balanced, and a weight of 2 N is then hung at its end A. At what distance from the point of suspension must a weight of 4 N be hung on the other side to bring the rod back into equilibrium?

Figure to be added

Figure for exercise 11.1 (1) — the 0.8 m rod AB suspended at its centre, with 2 N at the end A (0.4 m from the centre) and 4 N at an unknown distance x on the other side.

Solution

The rod is 0.8 m long, so the distance from the centre to A is 0.4 m.

moment produced by the 2 N = 2 N × 0.4 m = 0.8 N m

Let the distance at which the 4 N must hang be x.

4 × x = 0.8

x = 0.8 ÷ 4 = 0.2 m

You could have expected the distance to halve, since the force doubled: half of 0.4 m is 0.2 m.

Where is the distance measured from?

Distances are measured from the point of suspension, never from the end of the rod. The 0.8 m is the whole length of the rod, not a distance that goes into a moment.