Question

A solid disk, spinning counter-clockwise, has a mass of `16 kg` and a radius of `3/7 m`. If a point on the edge of the disk is moving at `7/5 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 `=4.81kgm^2s^-1` and the angular velocity is `=3.27rads^-1`

Explanation:

The angular velocity is

`omega=(Deltatheta)/(Deltat)`

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

`omega=v/r`

where,

`v=7/5ms^(-1)`

`r=3/7m`

So,

The angular velocity is

`omega=(7/5)/(3/7)=3.27rads^-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= 16kg`

So, `I=16*(3/7)^2/2=1.47kgm^2`

The angular momentum is

`L=1.47*3.27=4.81kgm^2s^-1`