A solid disk, spinning counter-clockwise, has a mass of #7 kg# and a radius of #8/3 m#. If a point on the edge of the disk is moving at #1/4 m/s# in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

1 Answer
Jun 13, 2017

Answer:

The angular momentum is #=2.33kgm^2s^-1# and the angular velocity is #=0.09375rads^-1#

Explanation:

The angular velocity is

#omega=(Deltatheta)/(Deltat)#

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

#omega=v/r#

where,

#v=1/4ms^(-1)#

#r=8/3m#

So,

#omega=(1/4)/(8/3)=3/32=0.09375rads^-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*(8/3)^2/2=224/9kgm^2#

The angular momentum is

#L=224/9*3/32=7/3=2.33kgm^2s^-1#