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What is the relation between linear velocity( $v$ ) and angular velocity( $ω$ )?

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v = rω

ω = vr

r = vω

v^{2} = rω

answer is A.

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Detailed Solution

The relation between linear velocity and angular velocity is

v = rω

.
For a particle moving along a circular path. Then its velocity is given by

v = \frac{2 πr}{t}

Its angular velocity

ω = \frac{θ}{t}

\Rightarrow ω = \frac{2 π}{t}

\Rightarrow

θ = 2 π

(In Radian)
for a circle,
Then

v = (\frac{2 π}{t}) r

\Rightarrow v = ωr

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