How to find the final angular velocity

[zami]

Homework Statement

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

Homework Equations

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?

 

[BvU]

Hello zami,
What about the carousel itself ?

 

[zami]

This is the problem, I don't understand if it has mass 4m without the 4 people on it or with people on it. Is it possible to solve this problem if the carousel is massless?

 

[alejandromeira]

What's is te TOTAL initial Inertia? And the final? Where are the people at the begin?

I have used your equations and I have obtained the result.

 

[alejandromeira]

carrousel has a mas 4m is in the statemen of the problem. And also 4 people: 4m
Ok I can be wrong, but I've obtained the result with your equations
Edit: why you say that the final inertia I is zero? carrousel moves and in the statement say that has mass.

 

[zami]

Ic = 2*m*r^2
Ip = 4*m*r^2
Io =Ic+Ip = 6*m*r^2
L = ωo*Io = 6*m*r^2*ωo
angular momentum L is conserved
ω1 = L/Ip = 6*m*r^2*ωo/(2*m*r^2) = 3*ωo

I think I misunderstood the question at the beginning and assumed that the carousel is massless, but if it has mass = 4m without the 4 people this should be the right answer. I don't know if it is possible to answer this question if the carousel is massless.

 

[alejandromeira]

I have made the same calculus

 

[zami]

Great thanks, It was just me misunderstanding the question. Thanks for the help.