(a) Derive the mathematical relation that connects the arc length traced by a particle moving on a circular path to the angular displacement produced at the centre of the circle.
(b) Hence, show that when two particles move through the same angular displacement on concentric circular tracks of radii r1 and r2, the ratio of the distances travelled along the tracks equals r2r1.
(c) If the angular displacement of both particles is doubled without changing the radii, explain qualitatively how the arc lengths are affected. Justify your answer without doing any numerical calculation.