A cylinder has inner and outer radii of $9 cm$ and $16 cm$ , respectively, and a mass of $4 kg$ . If the cylinder's frequency of counterclockwise rotation about its center changes from $9 Hz$ to $6 Hz$ , by how much does its angular momentum change?

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Answer 1 · 2018-02-05T06:14:16

The change in angular momentum is $=1.27kgm^2s^-1$

The angular momentum is $L=Iomega$

and $omega$ is the angular velocity

The mass of the cylinder is $m=4kg$

The radii of the cylinder are $r_1=0.09m$ and $r_2=0.16m$

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

So, $I=4*((0.09^2+0.16^2))/2=0.0674kgm^2$

The change in angular velocity is

$Delta omega=Deltaf*2pi=(9-6) xx2pi=pirads^-1$

The change in angular momentum is

$DeltaL=IDelta omega=0.0674xx6pi=1.27kgm^2s^-1$

A cylinder has inner and outer radii of 9 cm9 cm and 16 cm16 cm, respectively, and a mass of 4 kg4 kg. If the cylinder's frequency of counterclockwise rotation about its center changes from 9 Hz9 Hz to 6 Hz6 Hz, by how much does its angular momentum change?