Question

Three objects: disk, cylinder, and sphere are each rotating at 5 rads/s about an axis through their center. If the mass and radius of each object is 5 kg and 2 m respectively.

(a) What is is the moment of inertia of each object?

(b) What is is the angular momentum of each object?

Answer 1

(a) Moment of inertia of the disk, I1 = MR2/2

= (5*22/2)

= 10 kg.m2

Moment of inertia of the cylinder, I2 = MR2/2

= (5*22/2)

= 10 kg.m2

Moment of inertia of the sphere, I3 = 2MR2/5

= (2*5*22/5)

= 8 kg.m2

(b) Angular momentum of an object with moment of inertia I and angular velocity w is

L = Iw

For disk, angular momentum, L1 = I1w

= (10*5)

= 50 kg.m2/s

For cylinder, angular momentum, L2 = I2w

= (10*5)

= 50 kg.m2/s

For sphere, angular momentum, L3 = I3w

= (8*5)

= 40 kg.m2/s