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.

increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.