Question

A solid disk, spinning counter-clockwise, has a mass of `12 kg` and a radius of `7/5 m`. If a point on the edge of the disk is moving at `8/3 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 `=81.3kgm^2s^-1` and the angular velocity is `=1.9rads^-1`

Explanation:

The angular velocity is

`omega=(Deltatheta)/(Deltat)`

`v=r*((Deltatheta)/(Deltat))=r omega`

`omega=v/r`

where,

`v=8/3ms^(-1)`

`r=7/5m`

So,

The angular velocity is

`omega=(8/3)/(7/5)=40/21=1.9rads^-1`

The angular momentum is `L=Iomega`

where `I` is the moment of inertia

The mass is `m=12kg`

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

So, `I=12*(8/3)^2/2=128/3kgm^2`

The angular momentum is

`L=128/3*1.9=81.3kgm^2s^-1`