Relativistic velocity summation function (#14357)

* Relativistic velocity summation function

The formula v2=(v1+v)/(1+v1*v/c^2) is implemented.

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* relativistic_velocity_summation function parameters explained

* Gave meaningful names to function parameters

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* Enhance docstring with reference link

Updated docstring to include a reference link for the velocity addition formula.

* updating DIRECTORY.md

* updating DIRECTORY.md

* Fix grammar in relativistic kinetic energy comments

Corrected minor grammatical errors in comments and documentation.

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: cclauss <cclauss@users.noreply.github.com>

Author: 3 people

DIRECTORY.md

@@ -1014,6 +1014,8 @@
   * [Coulombs Law](physics/coulombs_law.py)
   * [Doppler Frequency](physics/doppler_frequency.py)
   * [Escape Velocity](physics/escape_velocity.py)
+  * [Faraday Lenz Law](physics/faraday_lenz_law.py)
+  * [First Law Of Thermodynamics](physics/first_law_of_thermodynamics.py)
   * [Grahams Law](physics/grahams_law.py)
   * [Hamiltonian](physics/hamiltonian.py)
   * [Horizontal Projectile Motion](physics/horizontal_projectile_motion.py)
@@ -1023,6 +1025,7 @@
   * [Kinetic Energy](physics/kinetic_energy.py)
   * [Lens Formulae](physics/lens_formulae.py)
   * [Lorentz Transformation Four Vector](physics/lorentz_transformation_four_vector.py)
+  * [Magnetic Flux](physics/magnetic_flux.py)
   * [Malus Law](physics/malus_law.py)
   * [Mass Energy Equivalence](physics/mass_energy_equivalence.py)
   * [Maxwells Equations](physics/maxwells_equations.py)
@@ -1035,9 +1038,12 @@
   * [Photoelectric Effect](physics/photoelectric_effect.py)
   * [Potential Energy](physics/potential_energy.py)
   * [Rainfall Intensity](physics/rainfall_intensity.py)
+  * [Relativistic Kinetic Energy](physics/relativistic_kinetic_energy.py)
+  * [Relativistic Velocity Summation](physics/relativistic_velocity_summation.py)
   * [Reynolds Number](physics/reynolds_number.py)
   * [Rms Speed Of Molecule](physics/rms_speed_of_molecule.py)
   * [Shear Stress](physics/shear_stress.py)
+  * [Snells Law](physics/snells_law.py)
   * [Speed Of Sound](physics/speed_of_sound.py)
   * [Speeds Of Gas Molecules](physics/speeds_of_gas_molecules.py)
   * [Terminal Velocity](physics/terminal_velocity.py)

physics/relativistic_kinetic_energy.py

@@ -21,12 +21,12 @@
 
     y = 1 / sqrt(1 - v^2 / c^2)
 
-is the Lorentz factor. At speeds much smaller than c, this expression reduces to the
+is the Lorentz factor. At speeds much lower than c, this expression reduces to the
 classical formula K ≈ (1/2) m v^2, so the relativistic result agrees with Newtonian
-kinetic energy in the low velocity limit.The standard unit of kinetic energy is the
+kinetic energy in the low-velocity limit. The standard unit of kinetic energy is the
 joule, while the English unit of kinetic energy is the foot-pound.
 
-Reference : https://en.wikipedia.org/wiki/Kinetic_energy
+Reference: https://en.wikipedia.org/wiki/Kinetic_energy
 """
 
 from math import sqrt
@@ -56,9 +56,8 @@ def relativistic_kinetic_energy(mass: float, velocity: float) -> float:
 
     if mass < 0:
         raise ValueError("The mass of a body cannot be negative")
-    else:
-        gamma = 1 / sqrt(1 - (velocity**2 / c**2))
-        return (gamma - 1) * mass * c**2
+    gamma = 1 / sqrt(1 - (velocity**2 / c**2))
+    return (gamma - 1) * mass * c**2
 
 
 if __name__ == "__main__":

physics/relativistic_velocity_summation.py

@@ -0,0 +1,49 @@
+"""
+The relativistic velocity summation formula calculates the combined velocity v2 of
+an object moving at speed v1 relative to a frame that is itself moving at velocity v
+relative to an observer. I take the last one to be strictly lower than the speed of
+light.
+The formula is v2 = (v1 + v)/(1 + v1 * v / c**2)
+v1 - speed of the object relative to a moving frame
+v - speed of the moving frame
+c - speed of light in a vacuum
+v2 - speed of the object relative to an observer
+
+https://en.wikipedia.org/wiki/Velocity-addition_formula
+"""
+
+c = 299792458
+
+
+def relativistic_velocity_summation(
+    object_velocity: float, frame_velocity: float
+) -> float:
+    """
+    >>> relativistic_velocity_summation(200000000, 200000000)
+    276805111.0636436
+    >>> relativistic_velocity_summation(299792458, 100000000)
+    299792458.0
+    >>> relativistic_velocity_summation(100000000, 299792458)
+    Traceback (most recent call last):
+        ...
+    ValueError: Speeds must not exceed light speed...
+    """
+    if (
+        object_velocity > c
+        or frame_velocity >= c
+        or object_velocity < -c
+        or frame_velocity <= -c
+    ):
+        raise ValueError(
+            "Speeds must not exceed light speed, and "
+            "the frame speed must be lower than the light speed!"
+        )
+    numerator = object_velocity + frame_velocity
+    denominator = 1 + object_velocity * frame_velocity / c**2
+    return numerator / denominator
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()