Question

A solid disk, spinning counter-clockwise, has a mass of `5 kg` and a radius of `4 m`. If a point on the edge of the disk is moving at `7 m/s` in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

Answer 1

The angular momentum is `L=(140pi) kgm^2s^(-1)`
The angular velocity is `omega=(7/2pi) rads^(-1)`

Explanation:

The angular velocity is `omega=v/r`

`v=7ms^(-1)`

`r=4m`

So,

`omega=7/4*2pi rads^(-1)=7/2pi rads^(-1)`

The angular momentum is `L=Iomega`

Where,

`I=` moment of inertia

For a solid disc, `I=1/2mr^2`

`I=1/2*5*4*4=40 kgm^2`

The angular momentum is

`L=Iomega=40*7/2pikgm^2s^(-1)`

`L=140pi kgm^2s^(-1)`