Question

A cylinder has inner and outer radii of `9 cm` and `14 cm`, respectively, and a mass of `9 kg`. If the cylinder's frequency of counterclockwise rotation about its center changes from `5 Hz` to `7 Hz`, by how much does its angular momentum change?

Answer 1

The change in angular momentum is `=1.57kgms^-1`

Explanation:

The angular momentum is `L=Iomega`

where `I` is the moment of inertia

The mass of the cylinder is `m=9kg`

The radii of the cylinder are `r_1=0.09m` and `r_2=0.14m`

For the cylinder, `I=m(r_1^2+r_2^2)/2`

So, `I=9*(0.09^2+0.14^2)/2=0.12465kgm^2`

The change in angular velocity is

`Delta omega=Deltaf*2pi=(7-5)*2pi=4pirads^-1`

The change in angular momentum is

`DeltaL=I Delta omega=0.12465*4pi=1.57kgm^2s^-1`