Question

A cylinder has inner and outer radii of `8 cm` and `15 cm`, respectively, and a mass of `1 kg`. If the cylinder's frequency of counterclockwise rotation about its center changes from `15 Hz` to `12 Hz`, by how much does its angular momentum change?

Answer 1

The change in angular momentum is `=0.27kgm^2s^-1`

Explanation:

The angular momentum is `L=Iomega`

where `I` is the moment of inertia

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

The mass of the cylinder is `m=1 kg`

The radii are `r_1=0.08m` and `r_2=0.15m`

So, the moment of inertia is

`I=1*(0.08^2+0.15^2)/2=0.01445kgm^2`

The change in angular velocity is

`Deltaomega=2pi(15-12)=6pirads^-1`

The change in angular momentum is

`DeltaL=IDeltaomega=0.01445*6pi=0.27kgm^2s^-1`