Modern Physics
Length contraction at β = 0.9
High β shortens L = L₀/γ and raises m = γ m₀ on the readouts.
Length contraction at β = 0.9 — interactive Modern Physics simulation. High β shortens L = L₀/γ and raises m = γ m₀ on the readouts. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Length contraction
High β shortens L = L₀/γ and raises m = γ m₀ on the readouts.
A rocket at proper length L₀ moving at β along x is measured shorter in the lab: L = L₀/γ with γ = 1/√(1−β²). Press Play: the ship contracts once to L₀/γ and stays there — no oscillation back. The K_class vs K_rel chart shows how kinetic energy departs from ½mv² at the same β.
- L = L₀/γ
- Along motion
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
A 10-meter rocket flies past you at high speed. Do you measure its length as exactly 10 meters, longer, or shorter than that?
Predictions to weigh
- The same 10 meters — length doesn't depend on relative motion.
- Longer than 10 meters.
- Shorter — an object's length along its direction of motion appears contracted to an observer it's moving past.
Variable roles
What you set:
- Speed fraction β = v/c
What you measure:
- Lorentz factor γ
- Contracted length L (m)
How the investigation runs
- Open the length-contraction-rocket preset and press Reset. The rocket's proper (rest-frame) length is fixed at 10 m; its speed is β = 0.9.
- Enable the Lorentz factor and contracted-length readouts.
- Set the rocket's speed for each trial and record its contracted length as measured from your (stationary) frame.
Governing equation
Length Contraction — L = L₀/γ
An object's length measured along its direction of motion, as seen by a stationary observer, is contracted from its proper (rest-frame) length: L = L_proper/γ, where γ = 1/√(1 − β²) ≥ 1.
What the printable worksheet asks students to work out
- For one trial, compute γ = 1/√(1 − β²), then L = L_proper/γ using the proper length 10 m. Compare both to the table.
- Explain why length contraction only affects the dimension ALONG the direction of motion — a rocket's width and height (perpendicular to its velocity) stay unchanged, only its length shortens.
Where this shows up beyond the lab
- Just like time dilation, length contraction is symmetric: from the rocket pilot's own frame, it's Earth (and everything on it) that appears contracted along the direction of relative motion, while the rocket itself measures its normal 10 m length. Explain why this isn't a contradiction.
- This experiment's rocket moving at β = 0.9 has γ ≈ 2.29 — meaning both its length is compressed by that factor AND, if it carried a clock, that clock would run correspondingly slow (time dilation) by the same factor. Explain why time dilation and length contraction are really two faces of the same underlying spacetime geometry.
- AP Physics 2 — Unit 15: Modern Physics
- IB Physics — A.5 Galilean and special relativity
- General High School Physics — Modern physics intro
- NGSS High School Physics — Wave-particle duality of light
- Welcome to Length Contraction Rocket
- Select the relativity setup
- Press Play
- Shortened along motion
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.
Special Relativity: Time Dilation