Consider a particle moving along a circular path of constant radius r.
(i) Starting from the definition of one radian, derive the relation s=rθ connecting the arc length s with the angular displacement θ.
(ii) Using dimensional analysis, show that the angular displacement θ is dimensionless, i.e. its dimensional formula is M0L0T0.
(iii) If θ is dimensionless, why is it still convenient in physics to treat the radian as a unit? Give two clear reasons to justify your answer.