Question

A cylinder has inner and outer radii of `2 cm` and `4 cm`, respectively, and a mass of `1 kg`. If the cylinder's frequency of counterclockwise rotation about its center changes from `6 Hz` to `2 Hz`, by how much does its angular momentum change?

Answer 1

`ΔL=-0.008pi(kgm^2)/s`

Explanation:

The moment of inertia for the cylinder in your problem in :

`I=1/2m(r^2+R^2)=1/2*1*(0.02^2+0.04^2)=0.001kgm^2`

Let's calculate the change in angular velocity :

`Δω=2piΔf=2pi4=8pi(rads)/s`

Now let's caclulate the change in angular momentum :

`ΔL=IΔω=0,001*8π=0.008pi(kgm^2)/s`

To start with the angular momentum was a vector that was comming out of the screen if the cylinder was on the screen.

Now that its lowered the change is into the page so we mus have

`ΔL=-0.008pi(kgm^2)/s`