Question

obtain a relation between linear velocity and angular velocity....?????



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Answer 1

The greater the rotation angle in a given amount of time, the greater the angular velocity. Angular velocity ω is analogous to linear velocity v. We can write the relationship between linear velocity and angular velocity in two different ways: v=rω or ω=v/r.

Answer 2

Linear Velocity is denoted by 'v'

Angular Velocity is denoted by 'ω'

As,

$\theta = \frac{ l}{r}$

Differentiating both sides w.r.t time

$\frac{d \theta}{dt} = \frac{1}{r} \frac{dr}{dt}$

$\implies \omega = \frac{v}{r}$

$v = r \omega$