A cylinder has inner and outer radii of #3 cm# and #9 cm#, respectively, and a mass of #4 kg#. If the cylinder's frequency of counterclockwise rotation about its center changes from #9 Hz# to #3 Hz#, by how much does its angular momentum change?

1 Answer
Dec 1, 2017

Answer:

The change in angular momentum is #=0.68kgm^2s^-1#

Explanation:

The angular momentum is #L=Iomega#

where #I# is the moment of inertia

and #omega# is the angular velocity

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

The radii of the cylinder are #r_1=0.03m# and #r_2=0.09m#

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

So, #I=4*((0.03^2+0.09^2))/2=0.018kgm^2#

The change in angular velocity is

#Delta omega=Deltaf*2pi=(9-3) xx2pi=12pirads^-1#

The change in angular momentum is

#DeltaL=IDelta omega=0.018 xx12pi=0.68kgm^2s^-1#