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

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Answer 1 · 2017-07-19T16:03:15

$ΔL=-0.008pi(kgm^2)/s$

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

$ΔL=-0.008pi(kgm^2)/s$

A cylinder has inner and outer radii of 2 cm2cm2 cm and 4 cm4cm4 cm, respectively, and a mass of 1 kg1kg1 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 6 Hz6Hz6 Hz to 2 Hz2Hz2 Hz, by how much does its angular momentum change?