Asolid metal sphere of diameter d is spinning in a gravity-free region of space with an angular velocity of ω. the sphere is slowly heated until it reaches its melting temperature, at which point it flattens into a uniform disk of thickness d/2. by what factor is the angular velocity changed?

Explanation:

It is given that, a solid metal sphere of diameter D is spinning in a gravity-free region of space with an angular velocity of ω.The sphere is slowly heated until it reaches its melting temperature, at which point it flattens into a uniform disk of thickness D/2.

The angular momentum remains conserved in this case. The relation between the angular momentum and the angular velocity is given by :

Where

are moment of inertia of sphere and the disk respectively

Here, volume before = volume after

Initial angular momentum,

..........(1)

Final angular momentum,

............(2)

From equation (1) and (2) :

Hence, this is the required solution.

1 the 4 is sig