Question

A solid disk, spinning counter-clockwise, has a mass of `7 kg` and a radius of `1/2 m`. If a point on the edge of the disk is moving at `6/5 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 `=14.7kgm^2s^-1`
The angular velocity is `=2.4rads^-1`

Explanation:

The angular velocity is

`omega=(Deltatheta)/(Deltat)`

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

`omega=v/r`

where,

`v=6/5ms^(-1)`

`r=1/2m`

So,

`omega=(6/5)/(1/2)=2.4rads^-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*(1/2)^2/2=49/8kgm^2`

The angular momentum is

`L=49/8*2.4=14.7kgm^2s^-1`