A horizontal platform in the shape of a circular disk rotate

A horizontal platform in the shape of a circular disk rotates on a frictionless bearing about a vertical axle through the center of the disk. The platform has a mass of 143 kg, a radius of 1.83 m, and a rotational inertia of 239 kg·m² about the axis of rotation. A 51.0 kg student walks slowly from the rim of the platform toward the center. If the angular speed of the system is 1.60 rad/s when the student starts at the rim, what is the angular speed when she is 0.490 m from the center?

Solution

When student is on the rim then the angular momentum (Id + Is)w.
Here Id = rotational inertia of the disc = 239 and Is = inertia of student about axis = 51 x 1.83^1.83 = 170.79.
So (239+170.79) x w = 409.79 x 1.6 = 655.66 kg m^2 /s
When the student at a distance of 0.49 m, then the total inertia = 239 + 12.24 = 251.24
Hence the angular momentum with new angular speed w1 = 251..24 w1
By conservation, 251.24 w1 = 655.66
Hence the required w1 = 655.66/251.24 = 2.61 rad/s (nearly)