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Centripetal force

In uniform circular motion the speed is constant, but the direction changes. That requires an acceleration towards the centre, the centripetal acceleration. The force that provides it is called the centripetal force, and it is not an extra force beside the others. It is the sum of the forces towards the centre, for example the pull of a string or friction. Without such a force the body continues straight ahead.

Try it yourself

Centripetal acceleration

a = \frac{v^2}{r}

centripetal acceleration

F = \frac{mv^2}{r}

centripetal force

Symbols

$v$	orbital speed	m/s
$r$	radius	m
$m$	mass	kg
$F$	force towards the centre	N

Example

A body of 2 kg moves in a circle of radius 2 m at 4 m/s.

$a = 4^2/2 = 8$ m/s² and $F = 2 \cdot 4^2/2 = 16$ N.

Double the speed requires four times the force to keep the same radius.

Practise circular motion and gravitation for free →

← Horizontal throw · The law of gravitation →

Part of Physics 2: Circular motion and gravitation.