Length contraction simulation

An object moving relative to you is shorter along its direction of motion, by the factor 1/γ. It is not an optical illusion: every measurement you make in your frame gives the shorter length.

Interactive, free and runs in your browser. Part of the Special Relativity simulations.

What you will see

A ship at rest and an identical moving ship fly over lab rulers. The moving ship, and the ruler painted on its hull, shrink along the direction of travel only; height and width stay the same. The card shows L₀, L and the percentage shortening.

Try this

  1. At β = 0.6 the ship should read 80% of its rest length.
  2. At β = 0.8 it is 60%, i.e. 40% shorter.
  3. Push β to 0.99 and see how extreme it gets near c.

Common misconception

The ship does not get thinner or shorter in every direction. Contraction happens only along the direction of motion, and the crew on board measure their ship at its full proper length.

Exam-style question

A spaceship is 100 m long at rest. How long is it measured to be as it passes Earth at 0.6c?

γ = 1/√(1 − 0.36) = 1.25, so L = L₀/γ = 100 m / 1.25 = 80 m.

Key equations

  • L = L₀ / γ

Curriculum

AQA A-level physics (turning points), IB Physics A.5.

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