Center of Mass Frame question

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.
  • #1
Thefox14
40
0

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?
 
Physics news on Phys.org
  • #2
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.

Similar threads

Kinetic energy in center of mass reference frame
    • Introductory Physics Homework Help
Replies
3
Views
236
Calculate center of rotation of monocopter
    • Introductory Physics Homework Help
Replies
17
Views
724
Motion of center of mass under gravity
    • Introductory Physics Homework Help
Replies
10
Views
1K
Angular momentum of a disk about an axis parallel to center of mass axis
    • Introductory Physics Homework Help
Replies
5
Views
1K
Calculating the center of mass as an astronaut moves on a shuttle
    • Introductory Physics Homework Help
Replies
5
Views
1K
Calculating System Work and Displacement of Center of Mass
    • Introductory Physics Homework Help
Replies
15
Views
1K
Find velocities when a mass leaves a system of a rod with two masses
    • Introductory Physics Homework Help
Replies
10
Views
898
Spring-mediated dipole in a magnetic field
    • Introductory Physics Homework Help
Replies
31
Views
1K
Center of Mass to lab-frame
    • Introductory Physics Homework Help
Replies
7
Views
1K
Two Particles Connected by Massless Rod: Dynamics Analysis
    • Introductory Physics Homework Help
Replies
5
Views
909

Hot Threads

Recent Insights

Back
Top