Elastic Collision Center Frame Speed Point Tool

Description

Resolve a one-dimensional two-body state into its common center-of-mass velocity and signed relative velocities.

A mechanics calculation needs a coordinate frame, sign convention, and consistent force, length, mass, and time units. Vector projections, local balance terms, and ideal motion equations describe particular parts of a physical model. They do not automatically establish all equilibrium conditions or the validity of the model.

Resolve a one-dimensional two-body state into its common center-of-mass velocity and signed relative velocities.

When to use this tool

Use Elastic Collision Center Frame Speed Point when you need this particular projection, balance, frame conversion, or ideal-model component from supplied physical quantities.

How to use the tool and how it works

Enter firstMass, secondMass, firstVelocity, secondVelocity. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read centerVelocity, firstRelative, secondRelative. Use the output convention below.

For positive firstMass and secondMass return centerVelocity=(m1*v1+m2*v2)/(m1+m2), firstRelative=v1-centerVelocity, and secondRelative=v2-centerVelocity.^[1]

Input field	Meaning and units	Accepted input
firstMass	First Mass	Required. Finite number; strictly above 0.
secondMass	Second Mass	Required. Finite number; strictly above 0.
firstVelocity	First Velocity	Required. Finite number.
secondVelocity	Second Velocity	Required. Finite number.

Output field	Interpretation	Returned shape
centerVelocity	Center Velocity	Required. Finite number.
firstRelative	First Relative	Required. Finite number.
secondRelative	Second Relative	Required. Finite number.

json

{
  "input": {
    "firstMass": 1,
    "secondMass": 1,
    "firstVelocity": 3,
    "secondVelocity": 1
  },
  "output": {
    "centerVelocity": 2,
    "firstRelative": 1,
    "secondRelative": -1
  }
}

Limitations and assumptions

Velocities use one signed axis. This finds center-of-mass frame coordinates before or after any event; despite the tool name, it does not calculate elastic post-collision velocities or test energy conservation.
Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.

Alternative or Complementary methods

Use a complete force, motion, or energy model when a single contribution is insufficient. Check coordinate frames, idealizations, and dimensional consistency before combining calculated terms.

References

Calculation and input contract: physics/elastic-collision-center-frame-speed-point — tool.io

Similar or alternative tools

Physics: Collision Restitution Relative Speed
Apply the normal coefficient-of-restitution relation to a nonnegative approach speed under an explicitly passive 0..1 restitution model; not a collision impulse solver.
Physics: Kinetic Energy Reference Frame Delta
Compare nonrelativistic one-axis kinetic energies across a Galilean frame shift, including the signed energy change; no relativistic speeds or energy conservation claim.