The length measured along an object’s direction of motion is shorter than its proper length.
Difficulty
Intermediate
Read time
5 min
Prerequisites
Basic algebra, consistent units, and the stated model assumptions
Source
OpenStax, College Physics 2e, §28.3 (Paul Peter Urone and Roger Hinrichs)OpenFormulaGraph equation reference; FormuLab adaptation details and license are provided below.
Adapted from OpenFormulaGraph, under CC BY 4.0.
FormuLab adapted wording, notation, applicability conditions and topic placement, and expanded the numerical check into a worked example. The textbook section reference was corrected.
The length measured along an object’s direction of motion is shorter than its proper length. Measuring the moving length requires recording both endpoints simultaneously in the observer’s frame.
| Symbol | Meaning | Units |
|---|---|---|
| Length (contracted) | ||
| Length (proper) | ||
| Velocity | ||
| Speed of Light |
Relate proper length to a moving-frame measurement.
Compare lengths measured simultaneously in different inertial frames.
A rod has proper length 2.00 m and moves parallel to its length at the listed speed. Find its simultaneously measured moving length.
OpenFormulaGraph equation reference; FormuLab adaptation details and license are provided below.
Adapted from OpenFormulaGraph, under CC BY 4.0.
FormuLab adapted wording, notation, applicability conditions and topic placement, and expanded the numerical check into a worked example. The textbook section reference was corrected.
Assumptions
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