A solid disk, spinning counter-clockwise, has a mass of #12 kg# and a radius of #7/5 m#. If a point on the edge of the disk is moving at #8/3 m/s# in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

1 Answer
Nov 12, 2017

Answer:

The angular momentum is #=81.3kgm^2s^-1# and the angular velocity is #=1.9rads^-1#

Explanation:

The angular velocity is

#omega=(Deltatheta)/(Deltat)#

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

#omega=v/r#

where,

#v=8/3ms^(-1)#

#r=7/5m#

So,

The angular velocity is

#omega=(8/3)/(7/5)=40/21=1.9rads^-1#

The angular momentum is #L=Iomega#

where #I# is the moment of inertia

The mass is #m=12kg#

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

So, #I=12*(8/3)^2/2=128/3kgm^2#

The angular momentum is

#L=128/3*1.9=81.3kgm^2s^-1#