A cylinder has inner and outer radii of 4 cm4cm and 18 cm18cm, respectively, and a mass of 1 kg1kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 15 Hz15Hz to 16 Hz16Hz, by how much does its angular momentum change?

1 Answer
Nov 14, 2017

The change in angular momentum is =0.11kgm^2s^-1=0.11kgm2s1

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=1kgm=1kg

The radii of the cylinder are r_1=0.04mr1=0.04m and r_2=0.18mr2=0.18m

For the cylinder, the moment of inertia is I=m((r_1^2+r_2^2))/2I=m(r21+r22)2

So, I=1*((0.04^2+0.18^2))/2=0.017kgm^2I=1(0.042+0.182)2=0.017kgm2

The change in angular velocity is

Delta omega=Deltaf*2pi=(16-15) xx2pi=2pirads^-1

The change in angular momentum is

DeltaL=IDelta omega=0.017 xx2pi=0.11kgm^2s^-1