Circular motion

Objective. Resolve radial acceleration and centripetal force.

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Learn: the key idea

An object moving in a circle of radius r at constant speed v experiences acceleration directed towards the centre, with magnitude v²/r (or equivalently ω²r, using angular speed ω=v/r), even though its speed is unchanged. This centripetal acceleration requires a net force towards the centre, F = mv²/r, supplied in practice by tension, friction, gravity or a normal reaction depending on the context. For example, a conical pendulum relies on the horizontal component of tension to provide this centripetal force, while the vertical component balances gravity.

Worked example

A particle of mass 0.2kg moves in a horizontal circle of radius 0.5m at a constant speed of 4m/s. Find the magnitude of the centripetal force acting on the particle.

1 $Centripetal force formula: F = mv²/r$
2 $Substitute values: F = 0.2 \times 4² / 0.5$
3 $Compute numerator: 0.2 \times 16 = 3.2$
4 $Divide by radius: F = 3.2/0.5 = 6.4 N$

Answer: F = 6.4 N

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Common mistake. Students treat circular motion as having zero acceleration because speed is constant, forgetting that velocity is a vector and its direction constantly changes, producing a genuine (centripetal) acceleration. Constant speed does not mean constant velocity in circular motion.

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