Sec 3 Combined Science (Physics) Turning Effects notes

Push a door and it swings about its hinges — the pivot. The turning effect of your push is called a moment. Everyday moments: a spanner turning a bolt, a crowbar lifting a crate, pedals turning a bicycle crank, a steering wheel turning in your hands. Bigger force → bigger moment; same force further from the pivot → bigger moment — which is why door handles are placed far from the hinges and why a long spanner beats a short one.

Moment = force × perpendicular distance from the pivot to the line of action of the force, measured in newton metres (N m). The distance must be perpendicular — the shortest distance from the pivot to the force's line. Pushing a door edge-on (force pointing at the hinge) gives zero perpendicular distance and zero turning effect, however hard you push.

If the force is applied at an angle, the effective distance is the perpendicular one — the shortest distance from the pivot to the force's line of action. A force pulling along a lever towards the pivot turns nothing: its line passes through the pivot, perpendicular distance zero, moment zero. In this course the standard questions give forces perpendicular to the lever, so the distance along the lever is the perpendicular distance; angle cases are handled by quoting the perpendicular idea.

A body at rest with no rotation is balanced — and balance has one crisp rule, the principle of moments: for a body in equilibrium, the total clockwise moments about a pivot equal the total anticlockwise moments about that same pivot. The classic set-up is a metre rule pivoted at its centre with weights hanging at different positions: weight × distance on the left = weight × distance on the right.

Every part of an object has weight — every atom of it. But when calculating moments, all that distributed weight behaves as if it were concentrated at a single point: the centre of gravity. For a uniform regular object (a metre rule, a rectangular block) it sits at the geometric centre — which is why a uniform rule pivoted at its 50 cm mark balances with no extra moment from its own weight.

When a rule is pivoted off-centre, its own weight joins the moment balance: weight acts downwards at the centre of gravity, and its moment = weight × distance from the pivot. A uniform rule's centre of gravity is a property of the object — always at its middle, wherever the pivot sits.

For an irregular object (a lamina, a kettle lid, a cardboard shape) you cannot spot the centre of gravity by eye. The practical method: hang the object freely from one point; it settles with its centre of gravity directly below the pivot, so a vertical line drawn from that pivot passes through it. Repeat hanging from a second, different point and draw a second vertical line: the two lines cross at the centre of gravity.

Why it works: a freely hanging object is in equilibrium — its weight (acting at the centre of gravity) and the pivot's pull must be along the same vertical line, otherwise there would be a turning effect and the object would swing. Three plumb lines from three points make a tidy diagram and a reliable crossing point. The same logic explains the balance test: an object balanced on a fingertip sits with its centre of gravity directly above the finger.