First slide

Law of conservation of angular momentum

Question

A disc rotates freely with rotational kinetic energy E about a normal axis through centre. A ring having the same radius but double the mass of disc is now, gently placed on the disc. The new rotational kinetic energy of the system would be

Difficult

A

$\frac{E}{2}$
B

$\frac{E}{5}$
C

$\frac{2 E}{5}$
D

$\frac{E}{3}$

Solution

$E = \frac{L^{2}}{2 I} h e r e l = c o n s \tan t s o \frac{E_{1}}{E_{2}} = \frac{I_{2}}{I_{1}} i n i t i a l m o m e n t o f i n e r t i a = \frac{M R^{2}}{2} f i n a l m o m e n t o f i n e r t i a \frac{M R^{2}}{2} + 2 M R^{2} = \frac{5 M R^{2}}{2} E_{2} = \frac{E}{5}$

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