Question

A supernova results when a star that has used up all of its fuel undergoes an extremely violent explosion and its mass is blown outward. Consider the star, before the explosion, to be a solid sphere of radius R rotating with an angular speed of 2.0 rev/day. Once the star explodes its mass rapidly expands into a spherical shell. Assuming that all of the star's mass is contained within this spherical shell and there are no external torques acting on it, what is the angular speed of this mass when the radius of the spherical shell is 5.8R?

Answer 1

`\omega_f=0.0356 rev/day`

Step-by-step explanation:

Given:

Angular speed
`\omega_1=2\ rev/day`

Radius of the solid sphere = R

Radius of the spherical shell, R' = 5.8R

now the initial moment of inertia i.e the moment of inertia of the solid sphere is given as:

`I_i=(2)/(5)MR^2`

where, M is the mass of the solid sphere

Now, the final moment of inertia i.e the moment of inertia of the spherical shell is given as:

`I_f=(2)/(3)MR'^2`

or

`I_f=(2)/(3)M(5.8R)^2`

or

`I_f=22.426MR^2`

Now applying the concept of conservation of angular momentum

we get

`I_i\omega_i=I_f\omega_f`

substituting the values, we get

`(2)/(5)MR^2* 2=22.426* MR^2\omega_f`

or

`\omega_f=((2)/(5)* 2)/(22.426)=0.0356 rev/day`