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
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
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.
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, WB = 40 N
- Weight acting on mass = W
- Length of beam = 5 m
- Distance to pivot (from end of beam), dW = 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
(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
Step 4: Calculate the anticlockwise moment
Step 5: Equate the clockwise and anticlockwise moments to calculate
- 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