A cylinder has inner and outer radii of 4 cm4cm and 8 cm8cm, respectively, and a mass of 3 kg3kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 12 Hz12Hz to 7 Hz7Hz, by how much does its angular momentum change?

1 Answer
Mar 8, 2017

The change in angular momentum is =0.38kgm^2s^-1=0.38kgm2s1

Explanation:

The angular momentum is L=IomegaL=Iω

where II is the moment of inertia

For a cylinder, I=m(r_1^2+r_2^2)/2I=mr21+r222

So, I=3*(0.04^2+0.08^2)/2=0.012kgm^2I=30.042+0.0822=0.012kgm2

The change in angular momentum is

DeltaL=IDelta omega

The change in angular velocity is

Delta omega=(12-7)*2pi=10pirads^-1

The change in angular momentum is

DeltaL=0.012*10pi=0.38kgm^2s^-1