A cylinder has inner and outer radii of $9 cm$ and $11 cm$ , respectively, and a mass of $5 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $12 Hz$ to $2 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2017-10-27T15:01:16

The change in angular momentum is $=3.17kgm^2s^-1$

The angular momentum is $L=Iomega$

and $omega$ is the angular velocity

The mass of the cylinder is $m=5kg$

The radii of the cylinder are $r_1=0.09m$ and $r_2=0.11m$

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

So, $I=5*((0.09^2+0.11^2))/2=0.0505kgm^2$

The change in angular velocity is

$Delta omega=Deltaf*2pi=(12-2) xx2pi=20pirads^-1$

The change in angular momentum is

$DeltaL=IDelta omega=0.0505 xx20pi=3.17kgm^2s^-1$

A cylinder has inner and outer radii of 9 cm9 cm and 11 cm11 cm, respectively, and a mass of 5 kg5 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 12 Hz12 Hz to 2 Hz2 Hz, by how much does its angular momentum change?