The Principle of Moments
The Principle of Moments
- A balanced see-saw does not turn. The turning effects on it must be cancelling.
- That single idea, written down carefully, is the basis of beam and balance questions in the paper.
The principle
- The principle of moments: for an object in equilibrium, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about the same point.
- Check each force one at a time: which way is it trying to turn the object about your chosen point, clockwise or anticlockwise?
Definition
2 marksWhat is meant by the principle of moments?
Model answer: For an object in rotational equilibrium, the sum of the clockwise moments about a point equals the sum of the anticlockwise moments about the same point.
The written statement is worth two marks: (1) the object is in equilibrium, and (2) clockwise moments = anticlockwise moments about the same point. Leaving out either part loses a mark (9702/21/M/J/25 Q2(a)).
Worked example
Smallest case: is it balanced?
A 20 N force pushes down 2.0 m to the left of a pivot. A 40 N force pushes down 1.0 m to the right. Does the see-saw turn?
- Anticlockwise: .
- Clockwise: .
- Equal, so the see-saw is balanced.
Worked example
One change: find the unknown force
A beam is in equilibrium. A 20 N force acts 0.5 m from the pivot and a 10 N force acts 1.0 m from the pivot, both turning clockwise. A force X acts 0.8 m from the pivot on the other side. Find X.
- Clockwise total: .
- Anticlockwise: . Set them equal: , so .
A 30 N force acts 1.2 m from a pivot. What force acting on the other side, 0.80 m from the pivot, produces equilibrium?
Show worked answer
- Equate opposite moments: .
- .
Answer: 45 N.