### Question: Derive a relation between linear and angular velocities.

**ANSWER**

Let a
particle is moving along a circle. If the initial position of the particle is
at A and after a small interval of time ∆t, it reaches point B describing angle
∆θ. The linear displacement is equal to the length of arc AB = ∆s.** **

∆s is resulted due to the linear velocity of the particle which is along the tangent to the circumference of the circle. We know that ∆s = r ∆θ. Dividing both sides by ∆t,

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