A 4.00 kg hollow sphere (I = 2/3 MR²)is spinning with an angular velocity of 10.0 rad/s.The diameter of the sphere is 20.0 cm.The angular kinetic energy of the spinning sphere is A) 1.75 J. B) 1.50 J. C) 1.33 J. D) 0.90 J. E) 0.75 J.

Question

Quizplus · Accepted Answer

First, we need to find the moment of inertia of the hollow sphere using the given formula:

I = 2/3 MR^2

Since the diameter of the sphere is 20.0 cm, its radius is 10.0 cm or 0.10 m.

I = 2/3 (4.00 kg)(0.10 m)^2 = 8.00 x 10^-3 kg m^2

Next, we can use the formula for angular kinetic energy:

K_rot = 1/2 I ω^2

where ω is the angular velocity. Substituting the values, we get:

K_rot = 1/2 (8.00 x 10^-3 kg m^2) (10.0 rad/s)^2 = 0.800 J

Therefore, the answer is C, 1.33 J.

A 400 Kg Hollow Sphere (I = 2/3 MR2)is Spinning with with an Angular

A 400 Kg Hollow Sphere (I = 2/3 MR²)is Spinning with with an Angular