First slide

Dynamics of rotational motion about fixed axis

Question

A child is standing with folded hands at the centre of a platform rotating about its central axis. The K.E of the system is K. The child now stretches his arms so that the M.I of the system doubles. The K.E of the system now is

Moderate

A

2K
B

K/2
C

4K
D

K/4

Solution

Kinetic energy $\large k = \frac{{{L^2}}}{{2I}}$
$\large \Rightarrow \,k \propto \frac{1}{I}\left( \because {L = {\mathop{\rm co}\nolimits} ns\tan t} \right)$
$\large {I_2} = 2{I_1}$
$\large \frac{{{k_2}}}{{{k_1}}} = \frac{{{I_1}}}{{{I_2}}}\,\, \Rightarrow \,\frac{{{k_2}}}{k} = \frac{1}{2} \Rightarrow \,\,{k_2} = \frac{k}{2}$

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