Question

A copper disk at 850 degrees celsius rotating about its axis with an angular speed of 25 rad/s in the outer space. As the disk radiates infrared light, its temperature falls to 20 degrees celsius. No external torque acts on the disk. Does the angular speed of the disk change as it cools?

Answer 1

YES

As the temperature of the copper disk decreases so does its diameter. Now as the diameter decreases its moment of inertia also decreases. But for rotational motion angular momentum is always conserved. So to compensate for the loss of moment of inertia its angular velocity increases.

Let us prove this quantitatively.

If the initial radius of the disk be R0 and after cooling be R then by the process off thermal expansion/cooling we must have

is the coefficient of linear expansion of copper and is the change in temperature.

So according to the given data we have

So, by the principle of conservation of angular momentum we must have

I denotes the moment of inertia and denotes the angular velocity

So our assumption was correct. The angular velocity did increase due to cooling.