Learn5054Paper 1 · Multiple ChoiceMotion, forces and energyTurning effect and centre of gravity

Motion, forces and energy · Subtopic 6 of 10

Turning Effect and Centre of Gravity

A force can turn an object about a pivot: its moment is force $\times$ perpendicular distance from the pivot. When an object balances, the total clockwise moment equals the total anticlockwise moment. An object's weight acts at its centre of gravity; a low centre of gravity and wide base make it stable.

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Section 1 of 14

Learning objectives

Calculate the moment of a force about a pivot.
Apply the principle of moments to balanced objects.
State the two conditions for equilibrium.
Find the centre of gravity of a lamina and explain stability.

Pause and think

Why is a door handle placed on the side furthest from the hinges?

Section 2 of 14

Core idea

Start hereBalancing a see-saw

A small child can balance a heavy adult on a see-saw by sitting further out. Turning effect depends on force and distance from the pivot.

The big idea

Moment $=F\times d$ (perpendicular distance). Equilibrium: clockwise = anticlockwise moments and forces balance. Low centre of gravity and wide base: stable.

1. Principle of moments

A see-saw: moving the load changes its moment

distance d (m) = 0.50

It balances when

400d=600

, so

d=1.5

m. The heavier person sits closer to the pivot.

\sum\text{clockwise moments}=\sum\text{anticlockwise moments}

moment: force (N) × perpendicular distance from pivot (m), in N m.

Worked exampleSee-saw

400 N child 1.5 m left of the pivot; 300 N child on the right.

Goal: Distance for balance; pivot force.
Strategy: Moments; then vertical forces.

$400\times1.5=300\times d$
Anticlockwise = clockwise.
$d=2\text{ m}$
Solve.
$400+300=700\text{ N}$
Pivot pushes up to balance both weights.

Answer

2

700

N upward.

✓ CheckLighter child sits further out ✓.

Worked exampleWeighing a metre rule

Balanced at 40 cm with 2 N at 10 cm. Rule's weight acts at 50 cm.

Goal: Weight $W$ .
Strategy: Moments about the pivot.

$2\times30=W\times10$
Distances from 40 cm: 30 cm and 10 cm.
$W=6\text{ N}$
Solve.

Answer

6

✓ CheckHeavier rule balances with a shorter arm ✓.

2. Stability

Stability: a low, wide base is harder to tip

An object topples when its centre of gravity moves outside its base. Racing cars and buses keep their centres of gravity low.

When does it topple?

$\text{CG above the base}$
Weight's moment about the tipping edge turns it back: stable.
$\text{CG beyond the edge}$
Weight's moment turns it further over: topples.

Common misconceptionSlanted distance Use the perpendicular distance from the pivot to the line of the force.

Pause and think

Why is a long spanner easier to use?

Summary

Moment $=Fd$ .
Equilibrium: moments and forces balance.

Centre of gravity: Point where weight seems to act.

History"Give me a place to stand." Archimedes studied levers around

250

BC and supposedly said, "Give me a place to stand, and I shall move the Earth." With a long enough lever and a fixed pivot, a small force can produce a huge moment.

Fun factThe leaning tower stays up. The Tower of Pisa leans about

4^\circ

but doesn't fall because a vertical line from its centre of gravity still lands inside its base. Engineers in the

1990

s removed soil from under the high side to reduce the lean and keep it that way.

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