Question

What happens to the centripetal acceleration of a revolving body if you double the orbital speed v and half the angular velocity w?

Answer 1

Answer:

Acc = rw^2

Explanation:

Just use formula

result will be radius times omaga square.

see in attachment

Answer 2

The new centripetal acceleration is same as the initial acceleration.

Explanation:

The centripetal acceleration of a revolving body is given by :

$a=r\omega^2$

Since, orbital speed, $v=r\omega$

$a=(r\omega)\times \omega\\\\a=v\omega$.........(1)

r is the radius of circular path

$\omega$ is the angular speed

If the orbital speed is doubled, v'=2v and angular velocity is halved, $\omega'=\dfrac{\omega}{2}$. New centripetal acceleration becomes :

$a'=v'\omega'\\\\a'=2v\times \dfrac{\omega}{2}\\\\a'=r\omega\\\\a'=a$

So, the new centripetal acceleration is same as the initial acceleration.

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