First slide

Law of conservation of angular momentum

Question

A uniform disc of radius a and mass m is rotating freely with angular speed $ω$ in a horizontal plane about a smooth fixed vertical axis through its centre. A particle of mass m is suddenly attached to the rim of the disc and rotates with it. The new angular speed is

NA

A

$\frac{ω}{6}$
B

$\frac{ω}{3}$
C

$\frac{ω}{2}$
D

$\frac{ω}{5}$

Solution

From the conservation of angular momentum, $I ω_{1} = I_{2} ω_{2}$
$\Rightarrow ω_{2} = \frac{I_{1}}{I_{2}} ω_{1} = \frac{(\frac{1}{2} m a^{2})}{(\frac{1}{2} m a^{2}) + m a^{2}} ω = \frac{ω}{3}$

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