First slide

Law of conservation of angular momentum

Question

A circular turn table rotates about its normal axis with uniform angular speed . A circular thick layer of ice and of radius much smaller than the table - top rotates along with the table. The new angular speed of the table when ice starts melting is

Easy

A

$\large {\omega}'>\omega$
B

$\large {\omega}'<\omega$
C

$\large {\omega}'=\omega$
D

any of (1), (2) or (3)

Solution

From L.C.A.M; Iω = L = constant. $\large \Rightarrow \omega \propto\frac 1I$
As the ice melts, it takes the shape of a thin disc whose radius is gradually increasing. Since $\large I\propto r^2$ , angular velocity of the system gradually decreases. Hence option (2) is right.

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