Question

A star is rotating with a period of 10.0 days. It collapses with no loss in mass to a white dwarf with a radius of .001 of its original radius.
a) What is its initial angular velocity?
b) What is its angular velocity after collapse?

Answer 1

Answer:

Part a)

Initial angular speed of the star is

$\omega = 7.27 \times 10^{-6} rad/s$

Part b)

Final angular speed of the star after it collapse is given as

$\omega = 7.72 rad/s$

Explanation:

Part a)

As we know that angular speed is given as

$\omega = \frac{2\pi}{T}$

now we have

$\omega = \frac{2\pi}{10 (24 \times 3600)}$

$\omega = 7.27 \times 10^{-6} rad/s$

Part b)

As we know that star collapses due to its own force

So here we can say that angular momentum is conserved here

So we have

$I_1\omega_1 = I_2\omega_2$

$\frac{2}{5}MR^2 (7.27 \times 10^{-6}) = \frac{2}{5}M(0.001R)^2\omega$

$\omega = 7.72 rad/s$