### Question: Derive an equation to show the relation between linear and angular accelerations.

**ANSWER**

Consider a particle moving along a circular path. Let at any instant of time its initial linear velocity is **v _{i}**. If the velocity undergoes a change then after a time interval t, its final velocity is

**v**. Remember linear velocity is along tangent to the circular path. Hence, the linear acceleration of the particle is

_{f}But

This is the required relation.

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