A solid disk, spinning counter-clockwise, has a mass of #13 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?

1 Answer
Mar 27, 2017

Answer:

The angular momentum is #=5.94kgm^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=13kg#

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

So, #I=13*(4/7)^2/2=2.12kgm^2#

#L=I*omega=2.12*2.8=5.94kgm^2s^-1#