A cylinder has inner and outer radii of #12 cm# and #15 cm#, respectively, and a mass of #4 kg#. If the cylinder's frequency of rotation about its center changes from #5 Hz# to #8 Hz#, by how much does its angular momentum change?

1 Answer
Mar 6, 2018

Answer:

The change in angular momentum is #=38.4kgm^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=0.12m# and #r_2=0.15m#

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

So, #I=4*((0.12^2+0.15^2))/2=2.0369kgm^2#

The change in angular velocity is

#Delta omega=Deltaf*2pi=(8-5) xx2pi=6pirads^-1#

The change in angular momentum is

#DeltaL=IDelta omega=2.0369xx6pi=38.4kgm^2s^-1#