Circular motion

Anything moving in a circle is always changing direction, so it’s accelerating towards the centre even at a steady speed. A resultant force towards the centre, the centripetal force, causes this.

Key facts

  • Angular speed ω = 2π/T (rad/s); v = ωr.
  • Centripetal acceleration a = v²/r = ω²r.
  • Centripetal force F = mv²/r.
  • The force can be tension, friction, gravity or a normal reaction.

Worked examples

Example 1

A 0.5 kg ball on a 0.8 m string goes round 2 times a second. Find the tension (ignore gravity).

  1. T = 0.5 s, so ω = 2π ÷ 0.5 = 4π rad/s.
  2. F = mω²r = 0.5 × (4π)² × 0.8 ≈ 63.2 N

Answer: 63.2 N