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 rotational 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

The moment of inertia of a hollow sphere is given by:

I = 2/3 M R^2

Substituting the given values:

I = 2/3 (4.00 kg) (0.10 m)^2 = 0.0267 kg m^2

The rotational kinetic energy is given by:

Krot = 1/2 I ω^2

Substituting the given values:

Krot = 1/2 (0.0267 kg m^2) (10.0 rad/s)^2 = 1.335 J

Rounding to two significant figures, the answer is:

Krot = 1.33 J

Therefore, the best choice is C.

A 400 Kg Hollow Sphere (I = 2/3 MR2) Is Spinning

A 400 Kg Hollow Sphere (I = 2/3 MR²) Is Spinning