Question

Establish a relation between linear velocity and angular velocity in a uniform circular motion and explain the direction of the velocity.

Answer 1

The distance ‘s’ covered by a body travelling in an arc of radius Y and turning its radial line by ‘θ’ is given by s = r θ

Differentiating both sides w.r.t. time, we have \(\frac {ds}{dt} = r \frac{d\theta}{dt}\) 

i.e., v = rw

or Linear velocity = radius × angular velocity.

At each point the body moves along the tangent.

The presence of centripetal force F = \(\frac {mv^2}{r}\)makes the body to travel in the circular path. Thus, the direction of velocity is always along the tangent at any point in the circular path.