Question

When a star collapses it significantly shrinks in size and spins up. Consider a star with a mass of M = 3.3×10³¹ kg and an initial radius of R_i = 7.3×10⁶ km. If the initial period of rotation of the star is T_i = 35.1 days, find the new rotational period after it collapses to a final radius of R_f = 7.3×10³ km. Treat the star before and after the collapse as a solid sphere with uniform mass distribution (which is not true, of course, but good enough for an estimation).

The new rotational period of the star, T_f =

Find the ratio between the final and initial rotational kinetic energies of the star.

The factor by which the kinetic energy of the star increases, KE_f/KE_i =

The increase in the rotational kinetic energy of the star comes from gravity. How much work is done by the gravity force while collapsing the star?

The work done by gravity, W =

Answer 1

That is,

New rotational period of the star

In seconds it will be given as,

Using this in relation 6 the final angular speed of the star will be given as,

Now using relation 5 the initial kinetic energy of the star before collapse will be given as,

Similarly using relation 8 final kinetic energy of the star will be given as,

So factor by which kinetic energy increases is,

Now gravitational work done (W) is,