# 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?

Jul 19, 2017

ΔL=-0.008pi(kgm^2)/s

#### Explanation:

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

$I = \frac{1}{2} m \left({r}^{2} + {R}^{2}\right) = \frac{1}{2} \cdot 1 \cdot \left({0.02}^{2} + {0.04}^{2}\right) = 0.001 k g {m}^{2}$

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