Question

uniform solid sphere of radius R rotates about a diameter with an angular speed 536 radians/second. The sphere then collapses under the action of internal forces to a final radius R/2. What is the final angular speed of the sphere in radians/second?

Answer 1

ω₂ = 2144 rad/s

Step-by-step explanation:

angular speed = 536 radians/second

as, we all know the moment of inertia of solid sphere

`I_(sphere)= (2)/(5)MR^2`

here in the question two radius are given

by using angular momentum conservation

`I_1 \omega_1 = I_2 \omega_2`

`(2)/(5)MR_1^2 \omega_1 =(2)/(5)MR_2^2 \omega_2\\R^2* 536= (R^2)/(4)* \omega_2`

`\omega_2 = 4 * 536`

ω₂ = 2144 rad/s

Answer 2

2144 rad/s

Step-by-step explanation:

R1 = R

ω1 = 536 rad/s

R2 = R/2

ω2 = ?

Mass is M

By use of angular momentum remains constant if no external force is acting on the body.

I1 ω1 = I2 ω2

The moment of inertia of solid sphere is 12/5 MR^2

So, 2/5 x M R^2 x 536 = 2/5 x M (R/2)^2 x ω2

536 = ω2 / 4

ω2 = 2144 rad/s