A cylinder has inner and outer radii of #5 cm# and #6 cm#, respectively, and a mass of #8 kg#. If the cylinder's frequency of counterclockwise rotation about its center changes from #12 Hz# to #4 Hz#, by how much does its angular momentum change?

1 Answer
Sep 12, 2017

Answer:

The change in angular momentum is #=1.23kgm^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=8kg#

The radii of the cylinder are #r_1=0.05m# and #r_2=0.06m#

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

So, #I=8*(0.05^2+0.06^2)/2=0.0244kgm^2#

The change in angular velocity is

#Delta omega=Deltaf*2pi=(12-4)*2pi=16pirads^-1#

The change in angular momentum is

#DeltaL=I Delta omega=0.0244*16pi=1.23kgm^2s^-1#