A cylinder has inner and outer radii of #2 cm# and #3 cm#, respectively, and a mass of #1 kg#. If the cylinder's frequency of counterclockwise rotation about its center changes from #6 Hz# to #2 Hz#, by how much does its angular momentum change?

1 Answer
Jan 8, 2018

Answer:

The change in angular momentum is #=0.0163kgm^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=1kg#

The radii of the cylinder are #r_1=0.02m# and #r_2=0.03m#

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

So, #I=1*((0.02^2+0.03^2))/2=0.00065kgm^2#

The change in angular velocity is

#Delta omega=Deltaf*2pi=(6-2) xx2pi=8pirads^-1#

The change in angular momentum is

#DeltaL=IDelta omega=0.00065 xx8pi=0.0163kgm^2s^-1#