Center of Mass: Definition, 3D Calculation & Frame

Click For Summary
SUMMARY

The center of mass (CoM) is a crucial concept in physics, defined as the point where the mass of a system is concentrated. To calculate the CoM in three dimensions, especially at relativistic speeds, the formula modifies to include the Lorentz factor, expressed as mvcosθ/√(1 - v²/c²). The 'center of mass frame' refers to a coordinate system where the total momentum of the system is zero, allowing for simplified calculations of energy and momentum.

PREREQUISITES
  • Understanding of basic physics concepts, particularly mass and momentum.
  • Familiarity with three-dimensional coordinate systems.
  • Knowledge of relativistic physics, specifically the Lorentz transformation.
  • Proficiency in mathematical calculations involving trigonometric functions and square roots.
NEXT STEPS
  • Study the Lorentz transformation and its applications in relativistic physics.
  • Learn about the implications of the center of mass frame in particle physics.
  • Explore advanced topics in three-dimensional kinematics.
  • Investigate the relationship between energy and momentum in different reference frames.
USEFUL FOR

Students and professionals in physics, particularly those focusing on mechanics and relativity, as well as engineers working with systems involving high-speed motion.

Dgonzo15
Messages
14
Reaction score
0
What exactly is center of mass, and how do I calculate in three dimensions? Also, I need to know how to calculate it in three dimensions at relativistically high speeds?
Also, what do they mean by 'center of mass frame', as in the question "What are the energy and momentum in the center of mass frame?" Thanks.
 
Physics news on Phys.org
Hi Dgonzo15! :smile:
Dgonzo15 said:
What exactly is center of mass, and how do I calculate in three dimensions?

oh come on, you can look this up!

look it up somewhere, and if you don't understand, copy it or link to it, and tell us which bit you don't understand
Also, I need to know how to calculate it in three dimensions at relativistically high speeds

instead of mvcosθ, you have to use mvcosθ/√(1 - v2/c2)
Also, what do they mean by 'center of mass frame', as in the question "What are the energy and momentum in the center of mass frame?"

it means using a coordinate system (a "frame") in which the centre of mass is stationary :wink:
 
The c.o.m. frame is defined such that the total momentum P vanishes
 

Similar threads

High School Does gravitational force act on system or its components?
  • · Replies 5 ·
Replies
5
Views
2K
High School Earth Center of Mass: GR & Inertial Object Acceleration
  • · Replies 8 ·
Replies
8
Views
2K
High School Rotating disc: tidal relativity across surface of disc
  • · Replies 14 ·
Replies
14
Views
1K
Undergrad Time dilation from galactic gravitational mass
  • · Replies 49 ·
2
Replies
49
Views
6K
High School Understanding a Special-Relativity Frame and Comoving Center-of-Mass
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Meaning of the invariants built from the angular momentum tensor
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Does Conservation of Momentum & Energy Hold in the C.O.M. Reference Frame?
  • · Replies 4 ·
Replies
4
Views
1K
High School Why Does Matter Fall to Center of a Mass? Explained
  • · Replies 4 ·
Replies
4
Views
1K
High School Speed of light and this Accelerating Rocket scenario
  • · Replies 45 ·
2
Replies
45
Views
5K
Undergrad Reference frames, center of rotation, etc
  • · Replies 88 ·
3
Replies
88
Views
4K