Moments · Year 13
In Year 13 you learn: equilibrium of rods.
A moment is the turning effect of a force about a point. For an object to stay still, the forces must balance and so must the moments. That is how we find the forces on beams, bridges, ladders and see-saws. It also shows where the centre of mass of a shape lies.
Key facts
- Moment = force × perpendicular distance from the pivot, in N m. A force F at angle θ to a rod, a distance d from the pivot, has moment Fd sin θ.
- In equilibrium the resultant force is zero AND the total clockwise moment equals the total anticlockwise moment about any point.
- Take moments about a point where an unknown force acts, so that force drops out of the equation.
- A uniform rod’s weight acts at its midpoint. On the point of tipping about one support, the reaction at the other support is zero.
- Centre of mass of particles: x̄ = (Σmx)/(Σm). For laminas use areas, x̄ = (ΣAx)/(ΣA), and subtract any holes.
- A freely suspended object hangs with its centre of mass directly below the point of suspension.
Worked examples
Example 1
A uniform 6 m beam of weight 200 N rests on supports at A (its left end) and B, 1 m from its right end. A 300 N load sits 2 m from A. Find the reactions at A and B.
Answer: 260 N at A and 240 N at B