Question

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 1

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 :

$\therefore \: I \times \omega1 = I_{2} \times \omega2$

$= > \: I \times 60= \dfrac{3I}{2} \times \omega2$

$= > \: 60= \dfrac{3}{2} \times \omega2$

$= > \: \omega2 = \dfrac{60 \times 2}{3}$

$= > \: \omega2 = 40 \: rpm$

So, final angular velocity is 40 rpm.