A flat uniform circular disk (radius = 2.50 m, mass = 1.00 102 kg) is initially stationary. The disk is free to rotate in the horizontal plane about a frictionless axis perpendicular to the center of the disk. A 55.0-kg person, standing 1.10 m from the axis, begins to run on the disk in a circular path and has a tangential speed of 2.80 m/s relative to the ground.

(a) Find the resulting angular speed of the disk (in rad/s) and describe the direction of the rotation. HELP

Question

A flat uniform circular disk (radius = 2.50 m, mass = 1.00  102 kg) is initially stationary. The disk is free to rotate in the horizontal plane about a frictionless axis perpendicular to the center of the disk. A 55.0-kg person, standing 1.10 m from the axis, begins to run on the disk in a circular path and has a tangential speed of 2.80 m/s relative to the ground.

(a) Find the resulting angular speed of the disk (in rad/s) and describe the direction of the rotation.  HELP

anonymous · Answer

first we find the angular momentum imparted to the disk which is equal to the angular momentum of the man.
L=r x p
    1.1*55*2.8=169.4
now we divide this by the moment of inertia of the disk about the given axis which is MR^2/2 
where M is mass of the disk and R is the radius of the disk.
u will get the angular speed of the disk by this.
Now the direction of rotation of the disk will be opposite to the direction executed by the man
This is because newton's 3rd law.
the disk exers a forward force to help the man run and the man exerts a backward and equal force.