Equilibrium of a rigid body
Moments and equilibrium
- The moment of a force about a point = force × perpendicular distance (turning effect).
- Weight acts at the centre of mass.
- A rigid body is in equilibrium when both:
- the vector sum of forces is zero, and
- the sum of moments about any point is zero.
Practice
The moment of a force about a point is:
A moment measures turning effect = force × perpendicular distance from the point.
Practice
A rigid body is in equilibrium only if both the forces and the moments sum to zero.
Both conditions are needed: zero resultant force and zero resultant moment.
Toppling and sliding
- A body may be on the edge of toppling (turning over) or sliding (slipping).
- Example: a 4 m beam, weight 100 N, pivoted at A, force $F$ at B. Moments about A: $F\times4 = 100\times2$, so $F = 50$ N.
Practice
A uniform 4 m beam of weight 100 N is pivoted at A; a force F at B (4 m away) balances it. Moments about A: F×4 = 100×2. Find F (N).
F × 4 = 100 × 2 = 200, so F = 50 N.
You've got it
Key idea
- moment = force × perpendicular distance
- equilibrium: forces sum to zero and moments sum to zero
- weight acts at the centre of mass; watch for toppling/sliding