Particle collides totally inelastically with a vertical free rod

AI Thread Summary
In a totally inelastic collision, a particle of mass M collides with a vertical rod of the same mass, resulting in a combined system that rotates about its center of mass. The conservation of momentum and angular momentum principles are crucial for solving the problem. The center-of-mass velocity can be determined using these conservation laws, while the moment of inertia is calculated based on the combined masses and geometry. The angular speed of the system post-collision is derived from the moment of inertia and the linear velocity. Understanding the rotation point as the center of mass is essential for accurate calculations.
rbwang1225
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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?
 
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First form the two equations. Conservation of linear and Conservation of angular momentum. As there is no external force and Torque.
 
rbwang1225 said:

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.
 

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