General Case of Relative Velocities

In summary, the conversation discusses the general case of velocity addition in relativity, with a focus on the formula and a typo that may be present. The conversation also clarifies the meaning of the vectors involved and their representation in the formula.
  • #1
Quarlep
257
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
 
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  • #2
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?
 
  • #3
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.
 

Related to General Case of Relative Velocities

1. What is the General Case of Relative Velocities?

The General Case of Relative Velocities is a concept in physics that deals with the motion of two objects in relation to each other. It involves calculating the velocities of the two objects and their relative velocity, taking into account their direction and speed.

2. How is the General Case of Relative Velocities different from the Special Case?

The Special Case of Relative Velocities, also known as the Galilean Transformation, assumes that the two objects are moving in a straight line at constant speeds. The General Case takes into account the possibility of the objects moving in any direction and at varying speeds.

3. What is the formula for calculating the General Case of Relative Velocities?

The formula for calculating the General Case of Relative Velocities is V_AB = V_A + V_B, where V_AB is the relative velocity of object A with respect to object B, V_A is the velocity of object A, and V_B is the velocity of object B.

4. What is the importance of understanding the General Case of Relative Velocities?

Understanding the General Case of Relative Velocities is important in various fields of science and engineering, such as mechanics, astronomy, and navigation. It allows for accurate predictions and calculations of the movement of objects in relation to each other.

5. How is the General Case of Relative Velocities applied in real-life situations?

The General Case of Relative Velocities is applied in many real-life situations, such as determining the motion of planets in our solar system, calculating the speed and direction of objects in space missions, and predicting the movement of vehicles in traffic. It is also used in sports, such as calculating the speed and direction of a ball in a game of soccer or tennis.

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