Assignment of Variables Help | Speed Addition Eqn Explained

[polishdude20]

Assignment of Variables please Help!

Ok well I am very confused on what variables you assign for the velocity addition equation.
What is U' , U , and V? like let's say 2 rockets heading toward each other and I want to find the speed i see if I'm on one of those rockets.

Also as a bonus I always get To and T and Lo and L mixed up explain?

 

[Rasalhague]

Also as a bonus I always get To and T and Lo and L mixed up explain?

It depends on what convention your source is using, and a good textbook should explain clearly and unambiguously what its symbols mean, but one common convenion is to write

[tex]t=\gamma t_0[/itex]

(t equals gamma times t_o), where

$$\gamma = \frac{1}{\sqrt{1-(\frac{v}{c})^2}}$$

using t_o for the interval of time between two events which happen at the same place in one inertial reference frame, and t for the interval of time between those same two events according to another inertial reference frame moving at some speed, v, relative to the first. And c is the speed of light in a vacuum.

If I had no other clue, I'd guess that L_o and L were being used like this:

$$L=L_0 / \gamma$$

(L equals L_o divided by gamma), where L_o is the length of an object as measured in an inertial frame of reference in which this object is at rest (not moving), and L is its length in some other inertial reference frame, moving parallel to the object's length with speed v.

 

[Rasalhague]

The formula for composition of velocities, sometimes called the "velocity-addition formula", is an equation you can use if you already know the velocity of an object in one inertial reference frame, and you want to find out what the velocity of that same body is in some other inertial reference frame, moving with some velocity relative to the first inertial reference frame. Let's call the frame where you already know the velocity your "input frame", and the frame in which you want to know the velocity your "output frame" (because that's the output you want the formula to compute).

Probably your symbols are being used as follows: U' for the velocity of the object with respect to the output frame, U for the velocity of the object with respect to the input frame, and V for the output of the target frame with respect to the input frame. Then, in the simple case U and V are parallel and in opposite directions,

$$U'=\frac{U+V}{1+UV/(c^2)}$$

(c is the speed of light in a vacuum.) Some people use u and v like this, others use them the other way around. Conventions vary, so everyone should define their terms. If they don't, in this case, you might be able to guess what they mean by looking for the odd one out. In this version the two Us (one with a prime symbol, U', the other without, U) refer to the velocities of the object, while the letter that's different, V, refers to the velocity of the output frame wrt the input frame.