4 persons each with mass m stand out on the edge of the carousel that rotates with angular velocity W0. carousel has mass 4m, radius r and inertia I = 2mr^2. The 4 persons then go all the way to the center of the carousel.
Show that the final angular velocity W1 = 3W0
See figure: https://imgur.com/a/uHeg1E8
Li = Lf
IW1 = IW0
The Attempt at a Solution
I tried IW0 = IW1, but the inertia will become 0 because the radius is 0 when the masses are in the center?
2mr^2 * W0 = I * W1
W1 = 2mr^2 * W0 / I
But I is zero?