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A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is
Asked by ayush.gupta3052 | 10 Jul, 2021, 07:01: PM
Let i be initial moment of inertia of system and ωi be the initial angular speed of rotation .
Let be final moment of inertia of system and ωf be the final angular speed of rotation .
By Conservation of angular momentum , we have ,

ωi = f ωf ..................... (1)
Final moment of Inertia f = 2 i ...................... (2)
Hence , we get from eqn.(1) ,  ωf = (1/2)ωi

Final kinetic energy = (1/2) f ωf2 = (1/2) ( i ) [ (1/2)ωi ]2 = (1/4) ωi2

Hence Final kinetic energy becomes (1/4)th of initial kinetic energy
Answered by Thiyagarajan K | 10 Jul, 2021, 08:16: PM
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