Question

A solid disk, spinning counter-clockwise, has a mass of `3 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 `=28/5kgm^2s^(-1)`
The angular velocity is `=40/12 Hz`

Explanation:

mass `m=3 kg`

radius of solid disc `r=7/5 m`

Velocity on the edge `v=8/3ms^(-1)`

The angular velocity `omega=v/r Hz`

`omega=(8/3)/(7/5)=8/3*5/7=40/21 Hz`

The angular momentum `L=I*omega`

where `I=`moment of inertia

For a solid disc, `I=(mr^2)/2=3*49/25*1/2=147/50kgm^2`

So, angular momentum `L=I*omega=147/50*40/21=28/5kgm^2s^(-1)`