Particle collides totally inelastically with a vertical free rod

In summary, the problem involves a particle colliding inelastically with a uniform vertical rod and requires finding the center-of-mass velocity, moment of inertia about the center-of-mass, and angular speed of the system using the conservation of momentum and conservation of angular momentum equations.
  • #1
rbwang1225
118
0

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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  • #2
First form the two equations. Conservation of linear and Conservation of angular momentum. As there is no external force and Torque.
 
  • #3
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.
 

FAQ: Particle collides totally inelastically with a vertical free rod

What is a particle and a vertical free rod?

A particle is a small unit of matter that has mass and occupies space. A vertical free rod is a rigid object that can rotate freely about a vertical axis.

What does it mean for a particle to collide totally inelastically with a vertical free rod?

An inelastic collision is one where there is a loss of kinetic energy, and the objects involved stick together after the collision. In the case of a vertical free rod, this means that the particle and the rod will become stuck together and will rotate as one object after the collision.

How does the mass of the particle and the rod affect the collision?

The mass of the particle and the rod will determine the final velocity and rotational speed of the combined object after the collision. The heavier the objects, the slower the final velocity and rotational speed will be.

What is the conservation of momentum and how does it apply to this collision?

The conservation of momentum states that the total momentum of a closed system remains constant before and after a collision. In this case, the initial momentum of the particle will equal the final momentum of the combined particle and rod after the collision.

How is the coefficient of restitution related to this collision?

The coefficient of restitution is a measure of the elasticity of a collision. In a totally inelastic collision, the coefficient of restitution is 0, meaning there is no rebound or separation between the objects after the collision. In other words, the objects become stuck together. This applies to the collision between a particle and a vertical free rod.

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