Rotational Motion Question 209

Question: A child with mass m is standing at the edge of a playground merry-go-round (A large uniform disc which rotates in horizontal plane about a fixed vertical axis in parks) with moment of inertia Vs I, radius R, and initial angular velocity w. The child jumps off the edge of the merry-go-round with a velocity v with respect to the ground in direction tangent to periphery of the disc as shown. The new angular veloity of the merry-go-round is :

Options:

A) $\sqrt{\frac{I{{\omega }^{2}}-mv^{2}}{I}}$

B) $\sqrt{\frac{(I+mR^{2}){{\omega }^{2}}-mv^{2}}{I}}$

C) $\frac{I\omega -mvR}{I}$

D) $\frac{(I\omega -mR^{2})\omega -mvR}{I}$

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Answer:

Correct Answer: D

Solution:

[d] Let the angular velocity of disc after child jumps off.

be $\omega ‘$

$\therefore $ From conservation of angular momentum $(I+mR^{2})\omega =mvR+I\omega $.

$\therefore \omega ‘=\frac{(I+mR^{2})\omega +mvR}{I}$



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