First slide

Law of conservation of angular momentum

Question

A circular disc of mass m is revolving with angular velocity $ω$ along a line passing perpendicular to its centre. When a mass m is gently attached to the revolving disc, then what will be new angular velocity

Moderate

A

$ω \sqrt{3}$
B

$ω / 2$
C

$4 ω / 5$
D

$ω / 3$

Solution

For circular disc, $I = \frac{1}{2} {MR}^{2}$
$∴ L = Iω = \frac{1}{2} {mR}^{2} ω$
When a mass m is attached to the disc, then
$L^{'} = (\frac{1}{2} {mR}^{2} + {mR}^{2}) ω^{'} = \frac{3}{2} {mR}^{2} ω^{'}$
An angular momentum is conserved
$\begin{array}{l} L = L^{'} \\ ∴ \frac{1}{2} {mR}^{2} ω = \frac{3}{2} {mR}^{2} ω^{'} or ω^{,} = \frac{ω}{3} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App