A cylinder has inner and outer radii of #2 cm# and #4 cm#, respectively, and a mass of #12 kg#. If the cylinder's frequency of counterclockwise rotation about its center changes from #6 Hz# to #1 Hz#, by how much does its angular momentum change?

1 Answer
Nov 11, 2017

Answer:

The change in angular momentum is #=0.38kgm^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=12kg#

The radii of the cylinder are #r_1=0.02m# and #r_2=0.04m#

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

So, #I=12*((0.02^2+0.04^2))/2=0.012kgm^2#

The change in angular velocity is

#Delta omega=Deltaf*2pi=(6-1) xx2pi=10pirads^-1#

The change in angular momentum is

#DeltaL=IDelta omega=0.012 xx10pi=0.38kgm^2s^-1#