An object moves in a circular path of radius, r, with a constant velocity, V. Derive an expression for its acceleration.

The velocity change from a to B = v_B – v_A  or v_B + (-v_A).

In figure  above, PQ represents v_B in magnitude (v) and direction BD; QR represents   -v_A in magnitude (v) and direction (CA).

Velocity change = v_B + (-v_A)  = PR

When δt is small, the angle AOB or δθ is small;

Also angle PQR equal to δθ is small

PR or acceleration then points toward O, the centre of the circle.

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