Student on a Turntable

1. Apr 27, 2010

ernay

1. The problem statement, all variables and given/known data
A student of mass m=40 kg is standing on the edge of a uniform, frictionless turntable, with diameter d = 5m and mass M=400 kg. The student and the turntable are initially rotating counterclockwise together about a fixed axis through the center of the turntable with an angular velocity of wi = 2 rev/min.
The student now start to walk around the edge of the turntable so that the turntable comes to rest. What is the resulting speed v of the student relative to someone standing next to the turntable? In what direction is the student walking, clockwise or counter clockwise?

2. Relevant equations
conversion of rev/min to rad/s = rev/min * 1min/60s * 2(pi)/1rev
Conservation of angular momentum:
Li = Lf

3. The attempt at a solution
(Iturntable + Istudent)wi = Iturntable(wf) + Istudent(wfinal for student)
( (1/2)(400)(2.5)2 + (40)(2.5)2) (.209) = ( (1/2)(400)(2.5)2) (0) + ( (40)(2.5)2 ) wf

Solve for wf and I got 1.254 rad/s
Then use v = (r)wf = (2.5)(1.254) = 3.135 m/s
The student is walking in the counterclockwise direction

Can someone let me know if this is right? I thought it was too easy for a 30 point question

2. Apr 27, 2010

kuruman

I didn't plug in the numbers, but the method looks OK.