Question

A solid disk, spinning counter-clockwise, has a mass of `2 kg` and a radius of `5 m`. If a point on the edge of the disk is moving at `6 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 `=30kgm^2s^-1` and The angular velocity is `=1.2rads^-1`

Explanation:

The angular velocity is

`omega=(Deltatheta)/(Deltat)`

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

`omega=v/r`

where,

`v=6ms^(-1)`

`r=5m`

So,

The angular velocity is

`omega=(6)/(5)=1.2rads^-1`

The angular momentum is `L=Iomega`

where `I` is the moment of inertia

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

The mass of the disc is `m= 2kg`

So, the moment of inertia is

`I=2*(5)^2/2=25kgm^2`

The angular momentum is

`L=Iomega=25*1.2=30kgm^2s^-1`