Consider a particle executing uniform circular motion of radius and frequency .

PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

Consider a particle executing uniform circular motion of radius

r

and frequency

\nu

. (i) Starting from basic definitions, derive the relation

\omega = 2\pi\nu

. (ii) Hence obtain an expression for the linear speed of the particle in terms of

r

and

\nu

only. (iii) Using the result of part (ii), derive an expression for the centripetal acceleration of the particle solely in terms of

r

and

\nu

. State clearly any intermediate steps used.