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

Answer:

2144 rad/s

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

Answer 2

Answer:

ω₂ = 2144 rad/s

Explanation:

angular  speed =  536 radians/second

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

$I_{sphere}= \dfrac{2}{5}MR^2$

here in the question two radius are given

by using angular momentum conservation

$I_1 \omega_1 = I_2 \omega_2$

$\dfrac{2}{5}MR_1^2 \omega_1 =\dfrac{2}{5}MR_2^2 \omega_2\\R^2\times 536= \dfrac{R^2}{4}\times \omega_2$

$\omega_2 = 4 \times 536$

ω₂ = 2144 rad/s