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 #3 Hz#, by how much does its angular momentum change?

1 Answer
Oct 13, 2017

Answer:

The change in angular momentum is #=2.54kgm^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=0.09m# 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=(9-3)*2pi=12pirads^-1#

The change in angular momentum is

#DeltaL=I Delta omega=0.0674*12pi=2.54kgm^2s^-1#