A cylinder has inner and outer radii of #16 cm# and #21 cm#, respectively, and a mass of #3 kg#. If the cylinder's frequency of rotation about its center changes from #2 Hz# to #4 Hz#, by how much does its angular momentum change?

1 Answer
Jan 18, 2018

Answer:

The change in angular momentum is #=1.314kgm^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=3kg#

The radii of the cylinder are #r_1=0.16m# and #r_2=0.21m#

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

So, #I=3*((0.16^2+0.21^2))/2=0.10455kgm^2#

The change in angular velocity is

#Delta omega=Deltaf*2pi=(4-2) xx2pi=4pirads^-1#

The change in angular momentum is

#DeltaL=IDelta omega=0.10455xx4pi=1.314kgm^2s^-1#