Moments

Summary — What This Chapter Covers

• Moment of a force = force × perpendicular distance from the pivot. This is what makes things rotate rather than just slide.
• If the force isn't perpendicular to the pivot arm, you need the perpendicular component of the distance (using cosθ) — not the raw distance.
• Centre of gravity is the single point where you can imagine all of an object's weight acting.
• An object's stability depends on the position of its centre of gravity relative to its base — wide base + low centre of gravity = stable.
• The Principle of Moments: for a system in equilibrium, total clockwise moments about a point = total anticlockwise moments about that same point.

1. Calculating the Moment of a Force

Think about trying to loosen a stuck bolt with a spanner. If you push right next to the bolt, it barely budges. If you push at the far end of the spanner handle, it turns much more easily — even though you're using exactly the same amount of force. That "extra turning power" you get by pushing further from the pivot is exactly what a moment measures.

A moment is defined as the turning effect of a force. It happens whenever a force causes (or tries to cause) an object to rotate about some fixed point, called the pivot. The pivot could be a hinge, a nail, a see-saw's fulcrum, or any point you choose to take moments about.

The Basic Formula (Force Perpendicular to the Pivot Arm)

The SI unit is the newton metre (N m). Sometimes you'll see newton centimetre (N cm) used instead — that's fine, just make sure the force and distance units match whatever the question gives you, and stay consistent throughout your working.

When the Force Isn't Perpendicular

Here's where a lot of students trip up. The formula above only works cleanly when the force is applied at right angles to the line joining the pivot to the point where the force acts. In real life — like turning a spanner at an angle — the force is often applied at some other angle θ to that line.

In that case, the distance x in the diagram is not the perpendicular distance to the force — it's just the distance from the pivot to where the force is applied. To find the true turning effect, you need to find the component of that distance which is perpendicular to the force.

2. Centre of Gravity