(A Level) Motion in a circle

Learning objectives

Define the radian — the angle at the centre of a circle when the arc it cuts off is one radius long — and convert angular displacements between degrees and radians.

Describe angular speed ω and use ω = 2π/T and v = rω for an object in uniform circular motion.

Explain why a force of constant size that always acts at right angles to the velocity changes only the direction of motion, giving a centripetal acceleration and circular motion at steady speed.

Use a = rω² = v²/r and F = mrω² = mv²/r, identifying which real force — tension, friction, gravity or a normal contact force — provides the centripetal force.

Analyse horizontal and vertical circular motion, such as a car on a bend, a conical pendulum or a mass whirled on a string at the top and bottom of its path.