Particle collides totally inelastically with a vertical free rod

[rbwang1225]

Homework Statement

A particle of mass M moving on a frictionless surface with velocity $V_0$ collides totally inelastically with an uniform vertical rod of mass M and length L. After immediately the collision, what is the center-of-mass velocity, the moment of inertia about the center-of-mass, and the angular speed of the system.

Homework Equations

conservation of momentum and conservation of angular momentum
moment of inertia

The Attempt at a Solution

I am wondering what point does the particle+rod system will rotate about?

 

[darkxponent]

First form the two equations. Conservation of linear and Conservation of angular momentum. As there is no external force and Torque.

 

[Redbelly98]

The Attempt at a Solution

I am wondering what point does the particle+rod system will rotate about?

The problem statement mentions "the moment of inertia about the center-of-mass", so that is a pretty good clue.