# V=? for Relativistic Mass,length contraction & time dilation

• Axidecimal
In summary: Once you have the equations down, you can use any letters that you want.In summary, the student found equations on a website that looked similar to the equations they were taught in class, but they were not the same. They needed to understand how to use the equations in order to solve for a variable. Once they had the equations down, they were able to use any letter they wanted.
Axidecimal

## Homework Statement

Velocity Equations for Relativistic Mass,length contraction and time dilation.
I was able to figure out one. This is not for homework. I want to learn these equations for future reference.

## The Attempt at a Solution

Length Contraction : v = c √{1-(l'/lo)^2}
Time Dilation: ?
Mass: ?

Just so I understand how you are thinking so I can answer properly:
How did you work out the length-contraction equation? Why not do the same thing for time dilation?

Note: no such thing as "relativistic mass". Used to be a thing but it turns out not to be much of a useful concept.

Axidecimal
l'/lo = √{1-v^2/c^2}
(l'/lo)^2 = 1-v^2/c^2
1-(l'/lo)^2 = v^2/c^2
√{1-(l'/lo)^2} = v/c
c√{1-(l'/lo)^2} = v

Mass increase has not been discontinued in my program.

Last edited:
Why not do the same thing for time dilation?

OK you need to do relativistic mass for passing exams - just understand that it is an out of date concept.

Axidecimal

I just copied the equations from wiki to this platform but i now have come to realize they are the same.
This is pretty self explanatory. i was given equations from my lessons that were essentially the same but all look different so i got confused. I didnt even look at the wiki equations closely until now

Last edited:
Simon Bridge said:
OK you need to do relativistic mass for passing exams - just understand that it is an out of date concept.
Better still: Point your teachers to my Insight post What is relativistic mass and why it is not used much? or refer them to me. It is simply a concept that is not used in physics today and it is really just confusing people to use it. Unfortunately, the concept permeates much of the introductory physics literature - which often is not written by people with specialist knowledge on relativity - and therefore becomes used by teachers at pre-university and introductory university level.

Simon Bridge and Axidecimal
Axidecimal said:
View attachment 110045
I just copied the equations from wiki to this platform but i now have come to realize they are the same.
This is pretty self explanatory. i was given equations from my lessons that were essentially the same but all look different so i got confused. I didnt even look at the wiki equations closely until now
Well done.
The form of the equations is ##x = \frac{y}{\sqrt{1-z^2}}## and you want to solve for ##z##.
It does not matter what the actual letters are.

It is more important to understand how to use the equations - that is the hard part to get your head around.

## What is the formula for calculating relativistic mass?

The formula for calculating relativistic mass is m = m0 / √(1 - v^2/c^2), where m0 is the rest mass, v is the velocity, and c is the speed of light.

## What is length contraction in relativity?

Length contraction is the phenomenon of an object appearing shorter in the direction of its motion when observed from a stationary frame of reference. This is due to the effects of time dilation and relativistic mass, which cause objects to contract in the direction of motion.

## How does time dilation work in relativity?

Time dilation is the phenomenon of time appearing to pass slower for objects in motion compared to objects at rest. This is due to the effects of the speed of light being constant and the relative nature of time and space in relativity.

## What is the significance of the speed of light in relativity?

The speed of light, denoted by c, is a fundamental constant in relativity. It is the maximum speed at which all matter and information can travel, and is used to define the relationship between time, space, and energy in the theory of relativity.

## How does relativistic mass relate to rest mass?

Relativistic mass is the mass of an object as measured from a frame of reference in which the object is in motion. It is related to rest mass, which is the mass of an object at rest, through the formula m = m0 / √(1 - v^2/c^2). As the speed of the object approaches the speed of light, the relativistic mass approaches infinity while the rest mass remains constant.

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