Question

When some stars use up their fuel, they undergo a catastrophic explosion called a supernova. This explosion blows much or all of a star's mass outward, in the form of a rapidly expanding spherical shell. As a simple model of the supernova process, assume that the star is a solid sphere of radius R that is initially rotating at 2.4 revolutions per day. After the star explodes, find the angular velocity, in revolutions per day, of the expanding supernova shell when its radius is 4.3R. Assume that all of the star's original mass is contained in the shell.

Answer 1

Answer:

0.0768 revolutions per day

Explanation:

R = Radius

$\omega$ = Angular velocity

As the mass is conserved the angular momentum is conserved

$I_1\omega_1=I_2\omega_2\\\Rightarrow \frac{I_1}{I_2}=\frac{\omega_2}{\omega_1}$

Moment of intertia for solid sphere

$I_1=\frac{2}{5}MR^2\\\Rightarrow I_1=0.4MR^2$

Moment of intertia for hollow sphere

$I_2=\frac{2}{3}M(4.3R)^2\\\Rightarrow I_2=12.327MR^2$

Dividing the moment of inertia

$\frac{I_1}{I_1}=\frac{0.4MR^2}{12.327MR^2}\\\Rightarrow \frac{I_1}{I_2}=0.032$

From the first equation

$\omega_2=\omega_1\frac{I_1}{I_2}\\\Rightarrow \omega_2=2.4\times 0.032\\\Rightarrow \omega_2=0.0768\ rev\day$

The angular velocity, in revolutions per day, of the expanding supernova shell is 0.0768 revolutions per day