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Moment of Inertia of an Annular Disc

An angular im...

Question

An angular impulse of $20 N m s$ is applied to a hollow cylinder of mass $2 k g$ and radius $2 c m$ . The change in its angular speed is

A

25 r a d / s

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B

2.5 r a d / s

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C

250 r a d / s

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D

25000 r a d / s

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Solution

The correct option is D $25000 r a d / s$
Given mass $m = 2 k g$ , radius $r = 2 c m = 0.02 m$ and angular impulse $L = 20 N m s$ , Let angular speed is $ω$ .
Moment of Inertia of cylinder , $I = m r^{2} = 2 \times {0.02}^{2} = 0.0008$
$\Rightarrow L = I Δ ω$ $\Rightarrow 20 = 0.0008 Δ ω$
$\Rightarrow Δ ω = 25000$ $r a d / s$

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