Question

Conversion of angular velocity to linear velocity

Answer 1

Heya!!

Here is your answer : -

The relationship between angular velocity and linear velocity is as follows : -

v = r.omega

Here, v refers to linear velocity , omega refers to angular velocity, r refers to radius , and the . (dot) refers to multiplication sign.

$Proof of this relation is as follows : -$

To prove : -

v = r.omega

Here,
L.H.S = v

Simplyfying R.H.S : -

r .omega

We know omega = angular displacement ( theta)/ time

and, angular displacement ( theta ) = l / r

Substituting the values,

{(l/r)/t}.r
(l/r.t).r
l/t
,which is equal to v.

L.H.S. = R.H.S.

Hence proved .

-- Conversion of angular velocity to linear velocity : -

omega.r = v ( Ans )

Hope it helps you