General Case of Relative Velocities

  • Context: Undergrad 
  • Thread starter Thread starter Quarlep
  • Start date Start date
  • Tags Tags
    General Relative
Click For Summary
SUMMARY

The discussion centers on the general case of relative velocities in the context of relativity, specifically addressing the formula for velocity addition as presented on Wikipedia. Participants noted a potential typo in the formula, where two velocity vectors, ##\vec{v}_A## and ##\vec{v}_B##, are shown side by side in the denominator without a dot product indicated. It was confirmed that ##\vec{v}_{BA}## represents the velocity of B in the rest frame of A, necessitating the calculation of this vector based on known velocities.

PREREQUISITES
  • Understanding of vector mathematics
  • Familiarity with the principles of relativity
  • Knowledge of dot products in physics
  • Basic comprehension of velocity concepts
NEXT STEPS
  • Review the Wikipedia article on relative velocity for detailed examples
  • Study the mathematical derivation of velocity addition in special relativity
  • Learn about vector operations, specifically dot products and their applications
  • Explore case studies involving relative velocities in different inertial frames
USEFUL FOR

Physics students, educators, and anyone interested in the mathematical foundations of relativity and vector analysis will benefit from this discussion.

Quarlep
Messages
257
Reaction score
4
I was looking relative velocities and I saw General case in Relativity part.That part means every direction isn't it.
http://en.wikipedia.org/wiki/Relative_velocity
and in there B is the observer or A is the observer
Thanks
 
Physics news on Phys.org
Quarlep said:
I was looking relative velocities and I saw General case in Relativity part.That part means every direction isn't it.
http://en.wikipedia.org/wiki/Relative_velocity
and in there B is the observer or A is the observer
Thanks

With respect to the general case of velocity addition in the wiki, there appears to be a (typo) in the formula.

I see two vectors (velocity A and velocity B) side by side in the denominator of the fraction. Most likely this is a dot product but there is no dot between them.

Yes? No?
 
Quarlep said:
in there B is the observer or A is the observer

##\vec{v}_{BA}## is the velocity of B in the rest frame of A, which needs to be calculated; ##\vec{v}_A## and ##\vec{v}_B## are the velocities of A and B in some other frame, which are presumed to be known at the start of the calculation.

MikeLizzi said:
Most likely this is a dot product

Yes, there should be a dot between them.
 

Similar threads

Undergrad Why doesn't relativity of simultaneity lead to a contradiction?
  • · Replies 17 ·
Replies
17
Views
2K
Undergrad An alternative derivation of the equation of motion in General Relativity
  • · Replies 0 ·
Replies
0
Views
1K
Undergrad Does the metric in general relativity depend only on position because of the equivalence principle?
  • · Replies 16 ·
Replies
16
Views
2K
Graduate Relativistic Relative Velocity Comp.: Bini, D. et al. (1995)
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Is an accelerating frame the same as an inertial frame at a point?
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad Relational event horizons?
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Construct a Diagram that Illustrates The Galilean Law of Addition of Velocities
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad How relative is the magnetic field of a current carrying conductor?
  • · Replies 4 ·
Replies
4
Views
1K
Graduate Dirac's derivation of the action/Lagrangian for a free particle
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Scope of General Relativity: Assumptions & Implications
  • · Replies 22 ·
Replies
22
Views
3K