Question

A cylinder has inner and outer radii of `4 cm` and `8 cm`, respectively, and a mass of `3 kg`. If the cylinder's frequency of counterclockwise rotation about its center changes from `2 Hz` to `7 Hz`, by how much does its angular momentum change?

Answer 1

The angular momentum changes by `=0.38kgm^2s^-1`

Explanation:

The angular momentum is `L=Iomega`

where `I` is the moment of inertia

The mass, `m=3kg`

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

So, `I=3*((0.04^2+0.08^2))/2=0.012kgm^2`

The change in angular momentum is

`DeltaL=IDelta omega`

The change in angular velocity is

`Delta omega=(7-2)*2pi=(10pi)rads^-1`

The change in angular momentum is

`DeltaL=0.012*10pi=0.38kgm^2s^-1`