Question

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?

Answer 1

`"change of angular momentum="0,4428*pi`

Explanation:

`"change of angular momentum="I*Delta omega`
`I:"moment of inertia"`
`Delta omega:"change of angular velocity"`
`I=1/2*m*(a^2+b^2)"cylinder axis at center"`
`m:4 kg`
`a=12 cm=0,12 m`
`b=15 cm=0,15 m`
`I=1/ cancel(2)* cancel(4) ((0,12)^2+(0,15)^2)`
`I=2*(0,0144+0,0225)`
`I=2*0,0369`
`I=0,0738`
`Delta omega=omega_2-omega_1`
`Delta omega=2*pi*f_2-2*pi*f_1`
`Delta omega=2*pi(f_2-f_1)`
`f_1=5 Hz" "f_2=8 Hz`
`Delta omega=2*pi(8-5)`
`Delta omega=6*pi`

`"change of angular momentum="0,0738*6*pi`
`"change of angular momentum="0,4428*pi`