Question

A solid disk, spinning counter-clockwise, has a mass of `5 kg` and a radius of `6 m`. If a point on the edge of the disk is moving at `19 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 `=285.3kgm^2s^-1`. The angular velocity is `=3.17rads^-1`

Explanation:

The angular velocity is

`omega=(Deltatheta)/(Deltat)`

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

`omega=v/r`

where,

`v=19ms^(-1)`

`r=6m`

So,

The angular velocity is

`omega=(19)/(6)=3.17rads^-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= 5kg`

So, the moment of inertia is

`I=5*(6)^2/2=90kgm^2`

The angular momentum is

`L=Iomega=90*3.17=285.3kgm^2s^-1`