A cylinder has inner and outer radii of #4 cm# and #5 cm#, respectively, and a mass of #5 kg#. If the cylinder's frequency of counterclockwise rotation about its center changes from #12 Hz# to #9 Hz#, by how much does its angular momentum change?

1 Answer
Sep 13, 2017

Answer:

The change in angular momentum is #=0.19kgm^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=5kg#

The radii of the cylinder are #r_1=0.04m# and #r_2=0.05m#

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

So, #I=5*(0.04^2+0.05^2)/2=0.01025kgm^2#

The change in angular velocity is

#Delta omega=Deltaf*2pi=(12-9)*2pi=6pirads^-1#

The change in angular momentum is

#DeltaL=I Delta omega=0.01025*6pi=0.19kgm^2s^-1#