Question 471: Centre of Mass and Rotational Motion

Question

A person of 80 kg mass is standing on the rim
of a circular platform of mass 200 kg rotating
about its axis at 5 revolutions per minute (rpm).
The person now starts moving towards the
centre of the platform. What will be the
rotational speed (in rpm) of the platform when
the person reaches its centre _________.

Accepted Answer

$${I_1}{\omega _1} = {I_2}{\omega _2}$$
$$ \Rightarrow $$ $$\left( {{{M{R^2}} \over 2} + m{R^2}} ight){\omega _1} = {{M{R^2}} \over 2}{\omega _2}$$
$$ \Rightarrow $$ $$\left( {1 + {{2m{R^2}} \over {M{R^2}}}} ight){\omega _1} = {\omega _2}$$
$$ \Rightarrow $$ $$\left( {1 + {{2 	imes 80} \over {200}}} ight){\omega _1} = {\omega _2}$$
$$ \Rightarrow $$ $${\omega _2} = \left( {1.8} ight){\omega _1}$$
$$ \Rightarrow $$ 2$$\pi $$f
2
= 2$$\pi $$f
1
$$ 	imes $$ 1.8
$$ \Rightarrow $$ f
2
= 5 $$ 	imes $$ 1.8 = 9

Centre of Mass and Rotational Motion

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