# How to find the final angular velocity

## 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

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
Homework Helper
Hello zami,
What about the carousel itself ?

This is the problem, I dont 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?

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.

zami
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.

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 dont know if it is possible to answer this question if the carousel is massless.

I have made the same calculus

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