---
title: "Galilean Frame Switcher Interactive Lab | Sandbox Physics"
description: "Which quantities of motion change when the observer changes? Coordinates, momentum and energy depend on the observer; relative motion stays the same."
canonical_url: "https://sandboxphysics.com/labs/galilean-frames/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/galilean-frames/"
last_modified: "2026-11-05"
---

M006 · Observers & invariants

# Galilean Frame Switcher

**Which quantities of motion change when the observer changes?** Coordinates, momentum and energy depend on the observer; relative motion stays the same. Kinetic energy is least in the mass-centre frame.

Switch between platform, train and mass-centre observers. Drag the gliders, compare relative motion and find the observer with the least kinetic energy.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

Two noninteracting gliders follow parallel ideal guides; observers move at constant horizontal velocities.

Physics tutorial

## Subtract the observer’s velocity

**Background** A glider moving past a platform can be still beside a train moving at the same speed. Both observers describe the same motion.

**Why it matters** The velocity arrow changes when you board a different observer. The gap between the two gliders changes in exactly the same way for everyone.

Start with the essentials

- **Focus question**: Which observer sees A at rest, and which sees zero total momentum?
- **One-sentence intuition**: Riding alongside one glider removes its velocity from your view. Riding with the mass centre removes the momentum of the whole system; these are generally different choices.

### Core mathematical model

#### Translate the coordinates

$$
\begin{aligned}x_i^\prime&=x_i-Ut,\\ v_{x,i}^\prime&=v_{x,i}-U.\end{aligned}
$$

The coordinate origins coincide at the initial time. The observer moves horizontally at a constant velocity; time and the transverse coordinate stay the same.

#### Add both momenta

$$
\begin{aligned}P_x^\prime&=P_x-MU,\\ P_y^\prime&=P_y.\end{aligned}
$$

Total mass is the sum of the two glider masses. Subtracting the observer velocity from each body changes the total momentum by total mass times that velocity.

#### Find the energy minimum

$$
\begin{aligned}K^\prime&=K-UP_x+\tfrac12MU^2,\\ K^\prime&=K_{\mathrm{CM}}^\prime+K_{\mathrm{rel}},\\ K_{\mathrm{CM}}^\prime&=\frac{\lVert\mathbf P^\prime\rVert^2}{2M}.\end{aligned}
$$

The relative-motion energy uses velocities measured from the mass centre. It stays when the momentum of the whole system is zero. This minimum does not select an absolute rest frame.

#### Compare one glider with the other

$$
\begin{aligned}\mathbf r_{BA}^\prime&=\mathbf r_{BA},\\ \mathbf v_{BA}^\prime&=\mathbf v_{BA}.\end{aligned}
$$

The subscript means the position or velocity of B minus that of A. The observer correction cancels. Parallel tracks keep the gliders apart even when their horizontal coordinates coincide.

### Common difficulties

#### Being still beside A is not the same as following the whole system

**Typical misconception** If A stands still, the total momentum and kinetic energy must both vanish.

**Better mental model** B can still move in that frame. The mass-centre observer balances both momenta. Its kinetic energy vanishes only when there is no relative motion.

### Run the experiment

1. 01

   #### Ride alongside one glider

   Choose Ride alongside A, then switch between Platform and Train.

   **What to observe:** A’s velocity arrow disappears in the matching train frame. The laboratory ruler moves past it.

2. 02

   #### Find the lowest energy

   Drag across the observer-energy curve, then choose Mass centre.

   **What to observe:** The marker reaches the minimum when the total momentum vanishes. The relative-motion part of the energy bar usually remains.

3. 03

   #### Keep the same position samples

   Open Position recording and inference, record positions and switch observers.

   **What to observe:** The raw laboratory rows and their error are unchanged. Estimated velocities subtract the new observer velocity from slopes of those same rows.

Physical conclusion

Specify the observer before quoting a velocity, momentum or kinetic energy. Relative position and relative velocity describe the same encounter in every constant-velocity frame.

Physical model, position data and sources

The two physical coordinates are horizontal; the vertical axis points up. Position is in metres, velocity in metres per second, mass in kilograms and energy in joules. Observer origins coincide at the initial time and move at constant horizontal velocities. Train and conveyor name observers; they exert no drive or friction on the bodies.

The gliders do not interact and follow separate parallel ideal guides. Gravity and vertical support balance; their horizontal accelerations are zero. Propulsion, air resistance and collisions with the track ends are omitted.

All apparatus lengths share one scale. The camera frames the selected run and can change its framing between observers; the numerical coordinates and ruler set the length reference. Velocity arrows start above the bodies for visibility and show one quarter-second of travel. The green cross is the mass-weighted centre, not a third particle.

On entry, position recording loads a simulated run. The CSV contains only timestamps, frame indices and laboratory positions with deterministic bounded coordinate error. Its noise is not a calibrated confidence model. Model curves and recorded dots are labelled separately. Changing the motion, masses or recording settings clears the rows; changing observer, time or slope window preserves them.

The inference uses only those rows, supplied masses, observer velocity and an odd centred least-squares window. Endpoints and gaps have no estimates. A window spanning contact averages the velocity jump and can underestimate instantaneous kinetic energy. The estimator never reads the model event time; it reports the time of the window’s centre sample.

- [OpenStax 4.5 — Relative motion](https://openstax.org/books/university-physics-volume-1/pages/4-5-relative-motion-in-one-and-two-dimensions)
- [OpenStax 9.6 — Centre of mass](https://openstax.org/books/university-physics-volume-1/pages/9-6-center-of-mass)
- [OpenStax 9.4 — Types of collision](https://openstax.org/books/university-physics-volume-1/pages/9-4-types-of-collisions)
- [MIT 16.07, Lecture 9 — Linear impulse, momentum and oblique collisions](https://ocw.mit.edu/courses/16-07-dynamics-fall-2009/a867999737497c79fd8ffe97641c503f_MIT16_07F09_Lec09.pdf)

Motion & dynamics · Starter path

## From a falling ball to an orbit

Start by measuring gravity and splitting motion into components. Then add contact forces and collisions, and follow the same laws all the way to an orbit.

[Start here → **Free Fall & Measuring Gravity** Capture a few drops and fit the camera positions to estimate gravitational acceleration. Then add air damping and watch the fit drift from the truth. Observe · 14 min](https://sandboxphysics.com/labs/free-fall/)

1. [1 Free Fall & Measuring Gravity](https://sandboxphysics.com/labs/free-fall/)
2. [2 Projectile Flight Designer](https://sandboxphysics.com/labs/projectile-flight/)
3. [3 Inclined Plane & Friction](https://sandboxphysics.com/labs/inclined-plane/)
4. [4 One-Dimensional Collision Bench](https://sandboxphysics.com/labs/collision-bench/)
5. [5 Mass–Spring Oscillator](https://sandboxphysics.com/labs/mass-spring/)
6. [6 How Orbits Take Shape](https://sandboxphysics.com/labs/orbit/)

[View the full path →](https://sandboxphysics.com/topics/mechanics/#starter-path)