Following a collision in outer space, a copper disk at $900$C is rotating about its axis with an angular speed of $27\mathrm{.}0$ rad$/$s$.$ As the disk radiates infrared light, its temperature falls to $20\mathrm{.}0$C$.$ No external torque acts on the disk.

$($a$)$ Does the angular speed change as the disk cools?

It stays the same.It increases.$$It decreases.

Explain how it changes or why it does not.

$($b$)$ What is its angular speed at the lower temperature?

rad$/$s