Principle of Moments | CIE International A Level Physics Revision Notes 2025

The principle of moments

The principle of moments states:

For a system to be in equilibrium, the sum of clockwise moments about a point must be equal to the sum of the anticlockwise moments (about the same point)

Moments acting on a balanced beam

Principle of moments, downloadable AS & A Level Physics revision notes

The sum of the anticlockwise moments of forces F₁ and F₃ are equal to the clockwise moment of force F₂

In the above diagram:
- Force F₂ is supplying a clockwise moment;
- Forces F₁ and F₃ are supplying anticlockwise moments
- The clockwise and anticlockwise moments are equal because the beam is in equilibrium

$F_{2} d_{2} = (F_{1} d_{1}) + (F_{3} d_{3})$

Worked example

A uniform beam of weight 40 N is 5 m long and is supported by a pivot situated 2 m from one end.

When a load of weight W is hung from that end, the beam is in equilibrium as shown in the diagram.

WE - principle of moments question image, downloadable AS & A Level Physics revision notes

What is the value of W?

A 10 N B 50 N C 25 N D 30 N

Answer:

Step 1: List the known quantities

Weight acting on beam, W_B = 40 N
Weight acting on mass = W
Length of beam = 5 m
Distance to pivot (from end of beam), d_W = 2 m

Step 2: Recall the principle of moments

clockwise moments = anticlockwise moments

Step 3: Calculate the clockwise moment

Because the beam is uniform, the force of weight acting upon it will be exerted from its centre of gravity
This will be the middle of the beam

$Centre of gravity = \frac{5}{2} = 2.5 m$ (from the end of the beam)

The pivot is 2 m from the end of the beam
Therefore, the force acts at a distance of 2.5 − 2 = 0.5 m from the pivot

4-2-1-we-principle-of-moments-answer-cie-new

$clockwise moment = W_{B} d$

$clockwise moment = 40 \times 0.5$

$clockwise moment = 20 N m$

Step 4: Calculate the anticlockwise moment

$anticlockwise moment = W d_{W}$

$anticlockwise moment = W \times 2 = 2 W$

Step 5: Equate the clockwise and anticlockwise moments to calculate

$clockwise moment = anticlockwise moment$

$20 = 2 W$

$W = \frac{20}{2} = 10 N$

Therefore, the answer is A

Examiner Tip

Make sure that all the distances are in the same units and you’re considering the correct forces as clockwise or anticlockwise, as seen in the diagram below Clockwise or anticlockwise moment, downloadable AS & A Level Physics revision notes

Principle of Moments (CIE A Level Physics)

Revision Note

The principle of moments

Moments acting on a balanced beam

Worked example

Examiner Tip

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Author: Leander