3.3.2—Circular acceleration

For uniform circular motion the velocity direction continually changes, so acceleration is directed towards the centre. Its magnitude is a=v²/r=rω².

The inward acceleration is supplied by the resultant inward force, not by a new separate force. Draw the radial direction first, then apply Newton’s second law along it.

A 0.50 kg mass moving at 3.0 m s⁻¹ on a 2.0 m radius circle needs a=4.5 m s⁻² inward and resultant force 2.25 N.

Constant speed does not mean zero acceleration; only the magnitude of velocity is constant, while its direction changes.