A cylinder has inner and outer radii of #9 cm# and #11 cm#, respectively, and a mass of #5 kg#. If the cylinder's frequency of counterclockwise rotation about its center changes from #12 Hz# to #2 Hz#, by how much does its angular momentum change?

1 Answer
Oct 27, 2017

Answer:

The change in angular momentum is #=3.17kgm^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=0.09m# and #r_2=0.11m#

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

So, #I=5*((0.09^2+0.11^2))/2=0.0505kgm^2#

The change in angular velocity is

#Delta omega=Deltaf*2pi=(12-2) xx2pi=20pirads^-1#

The change in angular momentum is

#DeltaL=IDelta omega=0.0505 xx20pi=3.17kgm^2s^-1#