Circular motion · Grade 9
Anything moving in a circle is always changing direction, so it is accelerating towards the centre even at a steady speed. A real force, such as friction, tension or gravity, must provide this centripetal force. Circular motion explains cars on bends, fairground rides and orbiting satellites.
Key facts
- Angular speed ω = (θ)/t = (2π)/T = 2πf (rad/s).
- Speed v = ωr = (2πr)/T.
- Centripetal acceleration a = (v²)/r = ω²r, towards the centre.
- Centripetal force F = (mv²)/r = mω²r, provided by a real force (friction, tension, gravity…).
- Vertical circle: at the top, mg + T = (mv²)/r. At the bottom, T − mg = (mv²)/r.
- Minimum speed at the top of a vertical loop: v = √(gr).