Question

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 `9 Hz`, by how much does its angular momentum change?

Answer 1

The change in angular momentum is `=4.6kgm^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=(9-2)*2pi=14pirads^-1`

The change in angular momentum is

`DeltaL=I Delta omega=0.10455*14pi=4.6kgm^2s^-1`