Question

A cylinder has inner and outer radii of `9 cm` and `12 cm`, respectively, and a mass of `9 kg`. If the cylinder's frequency of counterclockwise rotation about its center changes from `1 Hz` to `7 Hz`, by how much does its angular momentum change?

Answer 1

The change in angular momentum is `=7.63kgm^2s^-1`

Explanation:

The angular momentum is `L=Iomega`

where `I` is the moment of inertia

Mass, `m=9kg`

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

So, `I=9*((0.09^2+0.12^2))/2=0.2025kgm^2`

The change in angular momentum is

`DeltaL=IDelta omega`

The change in angular velocity is

`Delta omega=(7-1)*2pi=(12pi)rads^-1`

The change in angular momentum is

`DeltaL=0.2025*12pi=7.63kgm^2s^-1`