Question

A solid disk, spinning counter-clockwise, has a mass of `7 kg` and a radius of `8/3 m`. If a point on the edge of the disk is moving at `1/4 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 `=2.33kgm^2s^-1` and the angular velocity is `=0.09375rads^-1`

Explanation:

The angular velocity is

`omega=(Deltatheta)/(Deltat)`

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

`omega=v/r`

where,

`v=1/4ms^(-1)`

`r=8/3m`

So,

`omega=(1/4)/(8/3)=3/32=0.09375rads^-1`

The angular momentum is `L=Iomega`

where `I` is the moment of inertia

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

So, `I=7*(8/3)^2/2=224/9kgm^2`

The angular momentum is

`L=224/9*3/32=7/3=2.33kgm^2s^-1`