A cylinder has inner and outer radii of $2 cm$ and $6 cm$ , respectively, and a mass of $1 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $10 Hz$ to $15 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-09-06T05:36:49

The change in angular momentum is $=0.13kgm^2s^-1$

The angular momentum is $L=Iomega$

The mass of the cylinder is $m=1kg$

The radii of the cylinder are $r_1=0.02m$ and $r_2=0.06m$

For the cylinder, the moment of inertia is $I=m(r_1^2+r_2^2)/2$

So, $I=1*(0.02^2+0.06^2)/2=0.004kgm^2$

The change in angular velocity is

$Delta omega=Deltaf*2pi=(15-10)*2pi=10pirads^-1$

The change in angular momentum is

$DeltaL=I Delta omega=0.004*10pi=0.13kgm^2s^-1$

A cylinder has inner and outer radii of 2 cm2 cm and 6 cm6 cm, respectively, and a mass of 1 kg1 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 10 Hz10 Hz to 15 Hz15 Hz, by how much does its angular momentum change?