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Angular Displacement – 2011 A-level question

A disc rotates clockwise about its centre O until point P has moved to point Q, such that OP equals the length of the straight line PQ. What is the angular displacement of OQ relative to OP?

A.   $\frac{\pi}{3}$ rad

B.   $\frac{2\pi}{3}$ rad

C.   $\frac{4\pi}{3}$ rad

D.   $\frac{5\pi}{3}$ rad

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Answer: D.

The triangle OPQ is equilateral, so the angle $\angle QOP$ = 60° or $\dfrac{2\pi}{6}=\dfrac{\pi}{3}$ rad.

As OQ is displaced clockwise from OP, angular displacement $\theta = 2\pi – \dfrac{\pi}{3} = \dfrac{5\pi}{3}$ rad.

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