Question

If a trapeze artist rotates once each second while sailing through the air, and contracts to reduce her rotational inertia to one fourth of what it was, how many rotations per second will result?

Answer 1

Answer:

There are finally 4 rotations per second.

Explanation:

If a trapeze artist rotates once each second while sailing through the air, and contracts to reduce her rotational inertia to one fourth of what it was. We need to find the final angular velocity. It is a case of conservation of angular momentum such that :

$I_1\omega_1=I_2\omega_2$

Let $I_1=I$ , $I_2=\dfrac{I}{4}$ and $\omega_1=1$

So,

$\omega_2=\dfrac{I_1\omega_1}{I_2}$

$\omega_2=\dfrac{I\times 1}{(I/4)}$

$\omega_2=4\ rev/sec$

So, there are finally 4 rotations per second. Hence, this is the required solution.