Question

A cylinder has inner and outer radii of `12 cm` and `18 cm`, respectively, and a mass of `6 kg`. If the cylinder's frequency of rotation about its center changes from `7 Hz` to `6 Hz`, by how much does its angular momentum change?

Answer 1

`Delta P=-28,8pi`

Explanation:

`"1-calculate the changing of the angular velocity"`
`"2-calculate the moment of inertia for cylinder"`
`"3-calculate changing of the angular momentum"`

`"1)....................................................................."`
`f_i=7Hz" initial frequency"`
`f_l=6Hz" last frequency"`
`Delta omega=omega_l-omega_i" changing of the angular velocity"`

`omega_l=2*pi*f_l" "omega_l=2*pi*6" "omega_l=12pi " "(rad)/s`

`omega_i=2*pi*f_i" "omega_i=2*pi*7" "omega_i=14pi" "(rad)/s`

`Delta omega=12pi-14pi`

`Delta omega=-2pi" "(rad)/s`
`2)........................................................................`
`I=1/2*m(r_1^2+r_2^2)`
`"moment of inertia for cylinder which has inner and outer radius"`

m=6kg

`r_1=12 cm=0,12 m`
`r_1^2=1,44`

`r_2=18cm=0,18m`
`r_2^2=3,24`
`I=1/2*6(1,44+3,24)`

`I=3*4,68`

I=14,04

`3)............................................................................`
`Delta P=I*Delta omega" angular momentum change"`
`Delta P=-14,4*2pi`

`Delta P=-28,8pi`