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Answer» Relation between linear velocity and angular velocity
Let us consider a body P moving along the circumference of a circle of radius r with linear velocity V and angular velocity ω as shown in Fig.. Let it move from P to Q in TIME dt and dθ be the angle swept by the radius vector.
Let PQ = ds, be the arc length COVERED by the particle moving along the circle, then the angular displacement d θ is EXPRESSED as dθ = ds/r. But ds=vdt.
d θ/dt=v/r
(i.e) Angular velocity ω = v/r or v =ω r
In vector notation,
Vector v = Vector ω x Vector r

Thus, for a given angular velocity ω, the linear velocity v of the particle is directly proportional to the distance of the particle from the centre of the CIRCULAR path (i.e) for a body in a uniform circular motion, the angular velocity is the same for all points in the body but linear velocity is different for different points of the body.
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