Worked this out a few times, and I keep getting the answers completely wrong. No

Question

Worked this out a few times, and I keep getting the answers completely wrong. Not sure what I am doing wrong. Thanks

(a) After a student with mass m = 82.0 kg jumps onto the merry-go-round, the system's angular speed decreases to 1.95 rad/s. If the student walks slowly from the edge toward the center, find the angular speed of the system when she reaches a point 0.490 m from the center.
rad/s

(b) Find the change in the system's rotational kinetic energy caused by her movement to the center.
J

(c) Find the work done on the student as she walks to r = 0.490 m.
.J

Explanation / Answer

for a disk, moment of inertia about a vertical axis is givne by 0.5*mass*radius^2=244.8 kg.m^2

a)when the student jumps to the edge, the net moment of inertia becomes =244.8+82*2.4^2=717.12 kg.m^2

when she is 0.49 m from the center, net moment of inertia=244.8+82*0.49^2=264.48 kg.m^2

conserving angular momentum:
717.12*1.95=264.48*w

w=5.287 rad/sec

b)rotational kinetic energy is given by 0.5*moment of inertia*angular vleocity^2

initial rotational kinetic energy=1363.42 J

final rotational kinetic energy=3696.42 J

so change in kinetic energy=2333 J

c)work done=change in kinetic energy=2333 J

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