A cylinder has inner and outer radii of #8 cm# and #12 cm#, respectively, and a mass of #9 kg#. If the cylinder's frequency of counterclockwise rotation about its center changes from #1 Hz# to #7 Hz#, by how much does its angular momentum change?
1 Answer
Explanation:
Given:
1) A hollow cylinder radii:
2) Mass,
3)
Required change in angular momentum:
Theorem, Definition and Principles:
Angular Momentum,
Solution Strategy:
A) Compute the Moment of Inertia of Hollow cylinder
B) Convert frequency to radians:
C) Compute the Angular momentum for
Let
then we can derive the moment if inertia, I of HC as follows:
Also let
then
Now because we are dealing with HC,
Integrate over the inner and outer radiuses and inserting the expression for
Change