First slide

Angular momentum

Question

Two bodies have their moments of inertia I and 2 I respectively about their axis of rotation' If their kinetic energies of rotation are equal, their angular momenta will be in the ratio

Moderate

A

1 : 2
B

2 : 1
C

$\sqrt{2} : 1$
D

$1 : \sqrt{2}$

Solution

The kinetic energy of rotation K and angular momentum L are related as
$\begin{array}{l} K = \frac{L^{2}}{2 I} or L^{2} = 2 KI \\ ∴ \frac{L_{1}^{2}}{L_{7}^{2}} = \frac{2 K_{1} I_{1}}{2 K_{2} I_{2}} = \frac{KI}{K \times (2 I)} = \frac{1}{2} \end{array}$
or , $\frac{L_{1}}{L_{2}} = \sqrt{(\frac{1}{2})}$
or , $L_{1} : L_{2} = 1 : \sqrt{2}$

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