A person of 80kg mass is standing on the rim of a circular platform

Question:

A person of $80 \mathrm{~kg}$ mass is standing on the rim of a circular platform of mass $200 \mathrm{~kg}$ rotating about its axis as 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

Solution:

$\mathrm{L}_{\mathrm{i}}=\mathrm{L}_{\mathrm{f}}$

$\left(80 \mathrm{R}^{2}+\frac{200 \mathrm{R}^{2}}{2}\right) \omega=\left(0+\frac{200 \mathrm{R}^{2}}{2}\right) \omega_{1}$

$180 \omega_{0}=100 \omega_{1}$

$\omega_{1}=1.8 \omega_{0}=1.8 \times 5$

$=9 \mathrm{rpm}$

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