# What Defines the Total Momentum in the Center of Mass Frame?

• Thefox14
In summary, the center-of-mass frame is a frame of reference where the total momentum is always zero. This frame moves at the same velocity as the initial index particle, and in both the initial and final momentum vectors, there are equal and opposite pairs of equal magnitude. Therefore, the correct answers are D (a) and (b), and E (a) and (c). The concept may be confusing, but understanding the role of the center-of-mass frame is essential in studying momentum and collisions.
Thefox14

## Homework Statement

A key concept about the center-of-mass frame is that

A. the total momentum in the center of mass frame is always zero.
B. both the initial and final momentum vectors form pairs of equal magnitude and opposite direction
C. this frame always moves at the same velocity as the initial index particle
D. (a) and (b)
E. (a) and (c)
F. all of the above

2. The attempt at a solution

Currently I think it's A, as that's one of the key things about this frame, but what makes me uncertain is I'm not sure what an initial index particle is. I'm also pretty sure it's not C as that would only be true for elastic collisions correct?

Would someone be able to explain what an index particle is? Just knowing that would help a lot

## 1. What is the Center of Mass frame?

The Center of Mass frame, also known as the center of momentum frame, is a reference frame in which the total momentum of a system is zero. In this frame, the center of mass remains at rest and all other objects in the system move around it.

## 2. Why is the Center of Mass frame important?

The Center of Mass frame is important because it allows us to simplify the analysis of complex systems by reducing the number of variables. It is also a useful frame for studying collisions and interactions between objects.

## 3. How is the Center of Mass frame calculated?

The Center of Mass frame can be calculated using the formula: xCM = (m1x1 + m2x2 + ... + mnxn) / (m1 + m2 + ... + mn)Where xCM is the coordinate of the center of mass, mi is the mass of each object, and xi is the coordinate of each object along the chosen axis.

## 4. Can the Center of Mass frame be used for rotating systems?

Yes, the Center of Mass frame can be used for rotating systems as long as the axis of rotation is chosen as the reference axis. In this frame, the center of mass will remain at a fixed location while all other objects will rotate around it.

## 5. How does the Center of Mass frame relate to conservation of momentum?

The Center of Mass frame is closely related to conservation of momentum, as it is the frame in which the total momentum of a system is zero. This means that in this frame, the total momentum before and after a collision or interaction will be equal, as required by the law of conservation of momentum.

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