Respuesta :
Answer:
The angular velocity of the star after the collapse will be four times greater than its initial angular velocity.
Explanation:
Given:
The initial angular velocity of a spherical star is [tex]\omega[/tex].
The final radius of the star is half of its initial radius.
The conservation of the angular momentum is given by
[tex]I \omega = constant[/tex]
where [tex]I[/tex] is the moment of inertial of the star.
Consider that the initial moment of inertia of the star is [tex]I_{1}[/tex], the final moment of inertia is [tex]I_{2}[/tex] and the final angular velocity is [tex]\omega_{f}[/tex].
The moment of inertia of a sphere is given by
[tex]I = \dfrac{2}{5}MR^{2}[/tex]
where [tex]M[/tex] is the mass of the sphere and [tex]R[/tex] is the radius of the sphere.
The expression for the conservation of angular momentum for the star is given by
[tex]~~~~~&& I_{1} \omega = I_{2} \omega_{f}\\&or,& (\dfrac{2}{5}MR^{2}) \omega = (\dfrac{2}{5}M(\dfrac{R}{2})^{2}) \omega_{f}\\&or,& \omega_{f} = 4 \omega[/tex]
Thus, the angular velocity of the star after the collapse will be four times greater than its initial angular velocity.
