Calculating the Resulting Speed of a Student on a Turntable

[ernay]

Homework Statement

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 w_i = 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?

Homework Equations

conversion of rev/min to rad/s = rev/min * 1min/60s * 2(pi)/1rev
Conservation of angular momentum:
L_i = L_f

The Attempt at a Solution

(I_turntable + I_student)w_i = I_turntable(w_f) + I_student(w_{final for student})
( (1/2)(400)(2.5)² + (40)(2.5)²) (.209) = ( (1/2)(400)(2.5)²) (0) + ( (40)(2.5)² ) w_f

Solve for w_f and I got 1.254 rad/s
Then use v = (r)w_f = (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

 

[kuruman]

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