Question

A solid disk, spinning counter-clockwise, has a mass of `18 kg` and a radius of `4 m`. If a point on the edge of the disk is moving at `2/3 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 `=24kgm^2s^(-1)`
The angular velocity is `=1/6 Hz`

Explanation:

The angular velocity is `v=r omega`

`v=` velocity `=2/3ms^(-1)`

and `r=`radius `=4m`

So, angular velocity, `omega=v/r=2/3*1/4=1/6 Hz`

The angular momentum is `L=I*omega`

where `I=` moment of inertia

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

where `m=` the mass `=18 kg`

Therefore, `I=18*4*4/2=144 kg m^2`

So, the angular momentum is `L=144*1/6=24kgm^2s^(-1)`