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A vertical peg is attached to the edge of a horizontal disc of radius \( r \) and the disc rotates at constant angular speed \( \omega \) as shown in Fig.

A horizontal beam of parallel light produces a shadow of the peg on a screen as shown in Fig

At \( t=0 \), the peg is at \( \mathrm{P} \), producing a shadow on the screen at \( \mathrm{S} \). At time \( t \), the disc has rotated through angle \( \theta \). The peg is now at \( R \), producing a shadow at \( Q \).

Determine, in terms of \( \omega, t \) and \( r \), the distance SQ.
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