**Relation between Linear Velocity and Angular Velocity**

Suppose a particle of mass m moving in a circular path of radius r with constant speed v. let θ be the angular displacement when particle goes from points P to Q in time t as shown in the figure. If s is the arc of length PQ, then

θ = s/r

or, s = r. θ

Differentiating both sides with respect to time, we have

ds/dt = r. dθ/dt

As r is constant, v = ds/dt, and angular velocity, ω = dθ/dt

Then, above equation can be written as

V = r. ω

This is the relation between linear velocity and angular velocity.

Since linear acceleration is given by a = dv/dt

And angular acceleration is given by α = dω/dt

Differentiating both sides w.r.t time in V = r. ω, we get

a = r. α

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