3.4.1.2
The principle of moments: clockwise equals anticlockwise in equilibrium
Moments, Couples & Equilibrium — AQA A-Level Physics
Key Definition
Principle of moments — For a system in equilibrium, the sum of clockwise moments about any point equals the sum of anticlockwise moments about the same point.
- This applies to any pivot point -- you can choose the most convenient one.
- For a uniform beam, the weight acts at the centre (midpoint).
- Write the equation: sum of clockwise $moments = sum$ of anticlockwise moments, then solve for the unknown.
Worked Example
A uniform beam of weight 40 N is 5 m long, supported by a pivot 2 m from one end. A load W hangs from that end. The beam is in equilibriumAn object is in equilibrium when the resultant force on it is zero. The object is either stationary or moving at constant velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹... Find W.
Show Solution
1
Identify the clockwise moment
The beam is uniform, so its weight acts at the centre: 2.5 m from the end, which is 0.5 m from the pivot.
$$\text{Clockwise moment} = 40 \times 0.5 = 20 \text{ N m}$$2
Identify the anticlockwise moment
$$\text{Anticlockwise moment} = W \times 2$$
3
Apply the principle of momentsFor an object in rotational equilibriumAn object is in equilibrium when the resultant force on it is zero. The object is either stationary or moving at constant velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.., the sum of clockwise moments about any point equals the sum of anticlockwise moments about the same point.
$$20 = W \times 2$$
$$W = \frac{20}{2} = 10 \text{ N}$$Answer
$W = 10 N$
Examiner Tips and Tricks
- Make sure all distances are in the same units.
- Decide which direction is clockwise and which is anticlockwise from the diagram before writing your equation.
Related:Newton's Laws