A cylinder has inner and outer radii of 5 cm5cm and 6 cm6cm, respectively, and a mass of 8 kg8kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 12 Hz12Hz to 4 Hz4Hz, by how much does its angular momentum change?

1 Answer
Sep 12, 2017

The change in angular momentum is =1.23kgm^2s^-1=1.23kgm2s1

Explanation:

The angular momentum is L=IomegaL=Iω

where II is the moment of inertia

and omegaω is the angular velocity

The mass of the cylinder is m=8kgm=8kg

The radii of the cylinder are r_1=0.05mr1=0.05m and r_2=0.06mr2=0.06m

For the cylinder, the moment of inertia is I=m(r_1^2+r_2^2)/2I=mr21+r222

So, I=8*(0.05^2+0.06^2)/2=0.0244kgm^2I=80.052+0.0622=0.0244kgm2

The change in angular velocity is

Delta omega=Deltaf*2pi=(12-4)*2pi=16pirads^-1

The change in angular momentum is

DeltaL=I Delta omega=0.0244*16pi=1.23kgm^2s^-1