Home / Topics / Kinematics
Galilean transformation
Advanced
Position and velocity transform between frames moving at constant velocity.
x' = x − vtBetween frames at relative speed v: x' = x − vt, t' = t, and velocities add: u' = u − v. These hold at everyday speeds but fail near the speed of light, where Lorentz transformations are needed.
A train at 20 m/s and a passenger walking 2 m/s forward: the ground sees 22 m/s.
Galilean rules assume time is universal, which relativity shows is not exactly true.
In more detail
A Galilean transformation relates coordinates and velocities between frames moving at constant velocity relative to each other. Velocities add simply, which works well at everyday speeds.
Real-world uses
- Converting a car's speed from the road frame to a passenger's frame.
- Basic relative velocity problems in introductory mechanics.
- Physicists compare measurements made on a moving train and on the platform by transforming positions and velocities between the two frames.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
Where does it fail?
At speeds approaching the speed of light, where Lorentz transformations must be used.
Does time change in Galilean transformations?
No. Time is the same in all frames, which is an assumption that relativity revises.
Does the Galilean transformation work at very high speed?
Only at speeds much less than light. Near the speed of light, the Lorentz transformation of relativity is needed instead.
Related topics in Kinematics
Motion in polar coordinates · Motion in three dimensions · Parametric motion · Frames: inertial vs non-inertial · Coriolis and fictitious motion · Chase and meeting problems