Answer
(a) By putting his arms out, he puts more of his mass farther away from the axis of rotation, thus increasing his moment of inertia. Since angular momentum is conserved, the angular speed must decrease.
(b) The moment of inertia has increased by a factor of 1.5.
Work Step by Step
(a) By putting his arms out, he puts more of his mass farther away from the axis of rotation, thus increasing his moment of inertia. Since angular momentum is conserved, the angular speed must decrease.
(b) We can use conservation of angular momentum to solve this question.
$I_2~\omega_2 = I_1~\omega_1$
$\frac{I_2}{I_1} = \frac{\omega_1}{\omega_2} = \frac{0.90~rev/s}{0.60~rev/s} = 1.5$
The moment of inertia has increased by a factor of 1.5.
