Question

the angular velocity of a body under uniform circular motion is doubled without changing centripetal acceleration. If v was the original speed of the body, the new speed is - ? ​

Answer 1

Answer:

centripetal acceleration= velocity × angular velocity

a=vw

initially

a=vw

finally a=v1(2w)

on dividing

v1=v/2

Answer 2

Given:

The angular velocity of a body under uniform circular motion is doubled without changing centripetal acceleration.

To find:

New value of speed ?

Calculation:

Centripetal acceleration is constant :

$\therefore \: a_{c} = constant$

$\implies \: \dfrac{ {v}^{2} }{r} = constant$

$\implies \: v \times \dfrac{ v }{r} = constant$

$\implies \: v \times \omega = constant$

Now , let new speed be v_(2) :

$\therefore \: v \times \omega = v_{2} \times (2 \omega)$

$\implies\: v = 2 \times v_{2}$

$\implies\: v_{2} = \dfrac{v}{2}$

So, value of new speed when angular velocity is doubled is:

$\boxed{ \bold{\: v_{2} = \dfrac{v}{2} }}$