First slide

Law of conservation of angular momentum

Question

A thin solid disc of mass 1 kg and radius 25 cm is rotating about its own geometrical axis AB with angular velocity 12 rad/s. A particle of mass 1 kg is gently attached to the rim of the disc. Then new angular velocity of the disc is

Moderate

A

$6 rad/s$
B

$4 rad/s$
C

$3 rad/s$
D

$8 r a d / s$

Solution

Conserving angular momentum,
$(I_{1} + I_{2}) ω = I_{1} . ω_{0}$
$\Rightarrow ω = \frac{ω_{0}}{(1 + \frac{I_{2}}{I_{1}})} = \frac{R}{(1 + \frac{1 \times 25^{2}}{\frac{1}{2} \times 1 \times 25^{2}})} \frac{r a d}{s} = 4 \frac{r a d}{s}$

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