Question

A cylinder has inner and outer radii of `8 cm` and `16 cm`, respectively, and a mass of `6 kg`. If the cylinder's frequency of counterclockwise rotation about its center changes from `2 Hz` to `7 Hz`, by how much does its angular momentum change?

Answer 1

The nasty part of this problem is in coming up with the moment of inertia for a thick-walled cylinder rotating along an axis through its centre. This is

`I= m/2(r_1^2 +r_2^2)`

where `r_1` and `r_2` are the inner and outer radii, respectively.

In this case, `I= 6/2(.08^2 +.16^2)` = `0.096 kgm^2`

Now, the angular momentum is defined as the product of its moment of inertia multiplied by the angular momentum (in radians/s don't forget!).

`L=I` `omega`

Since 1 Hz is equivalent to 2`pi` radians, the angular velocity changes from 4`pi` to 14`pi`, and so, the change in angular momentum is found as follows:

`L_i = 0.096 xx 4"pi` = `0.384`pi#

`L_f = 0.096 xx 14"pi` = `1.344`pi#

`DeltaL = 0.960pi` `kgm^2/s`

(Hope you don't mind that I held back on the units until the last line. I thought they would make things a bit messy!)