A solid disk, spinning counter-clockwise, has a mass of #7 kg# and a radius of #5 m#. If a point on the edge of the disk is moving at #2 m/s# in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

1 Answer
Oct 29, 2017

Answer:

#omega=0.4color(white)is^-1#
#L=7color(white)ikgm^2s^-1#

Explanation:

Angular Velocity:

#omega=(Deltatheta)/(Deltat)#

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

So, #omega=v/r#

Here,

  • #v=2m/s#
  • #r=5m/#

#thereforeomega=(2m/s)/(5m)=0.4color(white)is^-1#

Angular Momentum:

#L=Iomega#

Here,

  • #I("moment of inertia")=(mr^2)/2#
    #=(7kg*(5m)^2)/2=17.5color(white)ikgm^2#
  • #omega=0.4color(white)i"rads"^-1#

#thereforeL=17.5color(white)ikgm^2*0.4color(white)i"rads"^-1#
#=7color(white)ikgm^2s^-1#