A ballet dancer spins about a vertical axis at 60 rpm with his arms cl

1.	A ballet dancer spins about a vertical axis at 60 rpm with his arms closed. Now he stretches his arms such that M.I. Increases by 50%. The new speed of revolution is?
Answer» Given: A ballet dancer spins about a vertical axis at 60 RPM with his arms closed. Now he stretches his arms such that M.I. Increases by 50%. To find: New angular velocity. Calculation: LET initial MOMENT of inertia be I , Hence, final moment of inertia will be $\therefore \: I_{2} = I + 50\%I$ $= > \: I_{2} = I + \dfrac{I}{2}$ $= > \: I_{2} = \dfrac{3I}{2}$ Now , applying conservation of angular momentum : $\therefore \: I \times \omega1 = I_{2} \times \omega2$ $= > \: I \times 60= \dfrac{3I}{2} \times \omega2$ $= > \: 60= \dfrac{3}{2} \times \omega2$ $= > \: \omega2 = \dfrac{60 \times 2}{3}$ $= > \: \omega2 = <klux>40</klux> \: rpm$ So, final angular velocity is 40 rpm.