Moment of force force perpendicular distance from the pivot:
Example 1 — moment of a force
A force of N acts at m from a pivot. Find the moment of force.
- .
Answer: N·m
Definition
A couple is a pair of equal, opposite, parallel forces whose lines of action don't coincide — it produces pure rotation, no net force.
Rule
First condition: the vector sum of all forces is zero (no linear acceleration).
Second condition: the sum of all moments (clockwise and anticlockwise) about any point is zero (no rotation) — the principle of moments.
Definition
Stable equilibrium: displaced slightly, a body returns to its original position (low, wide base). Unstable: displaced slightly, it moves further away (high centre of gravity). Neutral: displaced, it stays in its new position (e.g. a ball on a flat surface).
Example 2 — principle of moments
A beam balances with a N force at cm from the pivot on one side. What moment balances it on the other side?
- At balance, clockwise moment anticlockwise moment.
- Moment on the given side N·cm.
Answer: The other side's moment must also be N·cm
A screwdriver, a spanner and a beam balance are all everyday uses of moments: a longer handle (larger ) needs less force for the same turning effect.
Quick Recap
- ●Moment of force (perpendicular distance from the pivot)
- ●A couple: two equal, opposite, non-collinear forces — pure rotation
- ●Equilibrium: net force AND net moment
- ●Stable/unstable/neutral equilibrium depend on how the centre of gravity responds to a small displacement
- ●A longer handle needs less force for the same moment
