Question

Suppose our Sun eventually collapses into a white dwarf, in the process losing about two thirds of its mass and winding up with a radius 2.0 percent of its existing radius. What would its new rotation rate be? (Take the Sun's current period to be about 30 days.)
____ rad/s
What would be its final KE in terms of its initial KE of today?
(KE_final / KE_initial) = ____

Answer 1

Assuming the sun and white dwarf has a uniform density inside them.

The moment of inertia of the Sun

Where symbols have their usual meaning.

For the white dwarf, we know

and

So, the moment of inertia of the White dwarf

Now applying conservation of angular momentum

Putting this value in equation

So the rotation rate of the white dwarf is 1.818 x 10^-2 rad/s.

Initial rotational kinetic energy

Final rotational kinetic energy

So the ratio is 7500.