Question

A solid disk, spinning counter-clockwise, has a mass of `16 kg` and a radius of `4/7 m`. If a point on the edge of the disk is moving at `8/5 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 `=7.31kgm^2s^-1`
The angular velocity is `=2.8rads^-1`

Explanation:

The angular velocity is

`omega=(Deltatheta)/(Deltat)`

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

`omega=v/r`

where,

`v=8/5ms^(-1)`

`r=4/7m`

So,

The angular velocity is `omega=(8/5)/(4/7)=56/20=2.8rads^-1`

The angular momentum is `L=Iomega`

where `I` is the moment of inertia

mass, `m=16`

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

So, `I=16*(4/7)^2/2=2.61kgm^2`

`L=I*omega=2.61*2.8=7.31kgm^2s^-1`