Question

A cylinder has inner and outer radii of `9 cm` and `11 cm`, respectively, and a mass of `5 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 `=0.635kgm^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=5 kg`

The radii are `r_1=0.09m` and `r_2=0.11m`

So, the moment of inertia is

`I=5*(0.09^2+0.11^2)/2=0.0505kgm^2`

The change in angular velocity is

`Deltaomega=2pi(7-5)=4pirads^-1`

The change in angular momentum is

`DeltaL=IDeltaomega=0.0505*4pi=0.635kgm^2s^-1`