Relativistic Velocity Addition Calculator
This calculator helps physicists and students calculate the addition of velocities in the context of special relativity, solving the challenge of determining resultant velocities at high speeds.
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Data Source and Methodology
All calculations are rigorously based on the formulas and data provided by the Wikipedia page on Velocity Addition Formula. All calculations adhere strictly to these sources.
The Formula Explained
\( w = \frac{u + v}{1 + \frac{uv}{c^2}} \)
Glossary of Variables
- u: First velocity, as a fraction of the speed of light (c).
- v: Second velocity, as a fraction of the speed of light (c).
- w: Resultant velocity, as a fraction of the speed of light (c).
How It Works: A Step-by-Step Example
Consider two objects moving with velocities \( u = 0.5c \) and \( v = 0.4c \). Using the formula:
w = \frac{0.5 + 0.4}{1 + \frac{0.5 \times 0.4}{1}} = \frac{0.9}{1.2} = 0.75c
The resultant velocity \( w \) is \( 0.75c \).
Frequently Asked Questions (FAQ)
What is relativistic velocity addition?
It is the formula used to calculate the resultant velocity of two velocities in the context of special relativity.
Why is relativistic velocity addition important?
It is crucial in understanding motion at speeds close to the speed of light.
Can velocities exceed the speed of light?
No, according to Einstein's theory of relativity, the resultant velocity will always be less than the speed of light.
How does this calculator work?
It uses the velocity addition formula to compute the resultant velocity based on the inputs given as fractions of the speed of light.
Is this calculator accurate?
Yes, the calculator uses precise mathematical formulas to ensure accurate results.