Edexcel IAL · Mechanics 1
Moments
Maths — Mechanics 1 | Complete Revision Guide
The Big Idea: A moment measures a force's ability to rotate an object about a pivot — and when forces are balanced, clockwise moments always equal anti-clockwise moments.
What is a Moment?
Think of a moment as the "turning power" of a force. When you push a door open, you're applying a moment about the hinge. The further from the hinge you push, the easier it turns — that's exactly what the formula captures.
The moment of a force only exists relative to a specific point (called the pivot). Change the pivot, and the moment changes too.
Perpendicular distance! It must be the distance from the pivot measured at a right angle to the direction the force is acting — NOT just any distance along the object.
Force at an Angle — Using Trigonometry
If the force isn't perpendicular to the distance line, you first need to find the perpendicular component. The perpendicular distance becomes d sinθ, where θ is the angle between the force and the line from the pivot.
Force F (at angle θ)
\
\ ← perpendicular component = d·sinθ
\θ
─────────x─────────────────────
pivot P d metres
Moment about P = F × d·sinθ
Clockwise vs Anti-Clockwise
A force can spin an object clockwise ↻ or anti-clockwise ↺. To decide which way a force turns an object about a pivot, imagine a circle centred at the pivot, with the radius pointing from pivot to where the force acts. The force's direction tells you which way that circle spins.
Trick: Picture the pivot as the centre of a clock. If the force would push the "clock hand" (the radius) in the direction clock hands move → clockwise. Otherwise → anti-clockwise.
A zero moment occurs when the line of action of the force passes directly through the pivot — there's no turning effect because the perpendicular distance is zero.
Resultant Moment
When multiple forces act on an object, each creates a moment about any given pivot. The resultant moment is simply their algebraic sum:
- Choose a positive direction (clockwise or anti-clockwise) — state this clearly.
- Calculate each individual moment = F × perpendicular distance.
- Assign + to moments in your chosen direction, − to the opposite.
- Sum them all. The sign of the total tells you the direction of net rotation.
Worked Example 1 — Resultant Moment
Step 1 — Perpendicular distances: