Sec 3 Physics Turning Effects of Forces notes

Push a door at the edge opposite the hinges and it swings easily; push with the same force near the hinges and it barely moves. The difference is the moment — the turning effect of a force about a pivot (also called torque). It depends on both the size of the force and how far from the pivot it acts:

moment of a force = force × perpendicular distance from the pivot to the line of action of the force. The unit is the newton metre (N m). The word perpendicular carries the marks: only the part of the force that turns the body counts, measured as the shortest distance from the pivot to the force’s line of action. Everyday examples: a spanner (long handle, small hand force), a wheelbarrow (long handles lift a heavy load), a bicycle pedal (crank length sets the turning effect).

When a body is in equilibrium — not turning and not translating — the moments about any pivot balance. The principle of moments states: for a body in equilibrium, the sum of the clockwise moments about a point equals the sum of the anticlockwise moments about that point. Choose the pivot cleverly (usually through an unknown support force) and that force disappears from the equation.

1. 1Draw and label

   sketch the beam with every force and its distance from the pivot.

2. 2Choose the pivot

   usually through one unknown force, so its moment is zero.

3. 3Split the moments

   clockwise on one side, anticlockwise on the other; include the body’s own weight at its centre of gravity if the beam is not pivoted there.

4. 4Equate and solve

   clockwise sum = anticlockwise sum, then rearrange for the unknown.

5. 5Check the last force

   finish with total upward force = total downward force to find any remaining support force.

Every part of a body has weight, but the whole weight can be treated as acting at a single point: the centre of gravity. For a uniform regular body (a metre ruler, a flat square lamina) it sits at the geometric centre — which is why a ruler balances on a finger at its 50 cm mark. Irregular bodies have their centre of gravity shifted towards the heavier end.

To find the centre of gravity of a flat lamina: suspend it freely from a pin at one point; it settles with its centre of gravity directly below the pin (any other position gives the weight a restoring moment). Mark the vertical line with a plumb line, repeat from a second point, and the two lines cross at the centre of gravity.

In moment calculations, a uniform beam’s weight joins the equation at its midpoint. Forgetting that weight is the single most common mark-lost in beam problems — draw it on the diagram before writing any equation.

A full equilibrium argument checks two things separately: the forces balance (upward total = downward total) and the moments balance (clockwise total = anticlockwise total about any point). Structured questions often ask for both — the moment equation finds one unknown support force, and the force equation hands you the second for free.

The same two-step pattern answers "will it slide or topple first?" questions: compare the moment condition for toppling with the friction limit for sliding, and quote whichever limit arrives first. Examiners reward naming the failure mode explicitly, not just circling a number.

An object is stable when a small tilt produces forces that return it upright. Three states exist: stable (a small push and it returns), unstable (a small push and it topples further), and neutral (it stays where moved, like a ball on a level floor).

Two design levers control stability. A low centre of gravity means a tilt raises the centre only slightly before the weight’s line falls back inside the base, giving a restoring moment. A wide base gives the weight’s line further to travel before it leaves the footprint. This is why racing cars are built low and wide, why double-decker buses carry luggage on the lower deck and are tilt-tested with passengers upstairs, and why a brolly-standing umbrella falls while the same umbrella lying flat is unmovable.