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I know the solution to this problem, and I put it below to follow the forum's rules, but my problem is not with the solution. I ask the actual doubt at the bottom of this message.

## Homework Statement

A carousel has a radius of 2 m and a moment of inertia of 500 kg·m², and can rotate around a frictionless axis. A person of 25 kg runs tangentially towards the edge of this carousel, which is at rest, with an initial velocity

*v*= 2.5 m/s, and jumps into the toy. What is the final angular velocity of the person and the carousel together?

## Homework Equations

[tex]L=mvr[/tex]

[tex]I=mr^2[/tex]

## The Attempt at a Solution

Here is the solution, but it is actually not the doubt I have:

Since there is no external torque acting on the system, angular momentum is conserved. The initial angular momentum of the system is the person's angular momentum, since the carousel is at rest. Since the person runs tangentially towards the carousel, the distance from the axis of rotation perpendicular to the direction of motion is the radius of the carousel (R).

L

_{i}= mvR = (25)·(2.5)·(2) = 125 kg·m²/s

After the person jumps into the edge of the carousel, his moment of inertia is mr² = 25·2² = 100 kg·m²; the moment of inertia of the carousel is 500 kg·m²; so, the final angular momentum of the system is: L

_{f}= (100 + 500)ω

_{f}; equalling L

_{i}and L

_{f}, I find that ω

_{f}= 0.208 rad/s.

As I said, this is actually not the doubt yet. The doubt is: the book says that the

**linear**momentum is not conserved in the above situation. Why?