Question

A solid disk, spinning counter-clockwise, has a mass of `6 kg` and a radius of `8/5 m`. If a point on the edge of the disk is moving at `7/4 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 `=8.4kgm^2s^-1` and the angular velocity is `=1.094rads^-1`

Explanation:

The angular velocity is

`omega=(Deltatheta)/(Deltat)`

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

`omega=v/r`

where,

`v=7/4ms^(-1)`

`r=8/5m`

So,

The angular velocity is

`omega=(7/4)/(8/5)=35/32=1.094rads^-1`

The angular momentum is `L=Iomega`

where `I` is the moment of inertia

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

The mass is `m=6 kg`

So, `I=6*(8/5)^2/2=192/25kgm^2`

The angular momentum is

`L=192/25*1.094=8.4kgm^2s^-1`