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Units, Measurement and Dimensions

Strain has no units at all. Divide one length by another, and the units simply cancel out. This article covers dimensions and measurement in physics.

📑 Contents
✊ Must Know
Fundamental Quantities and Dimensions
  • Seven FundamentalsPhysics has seven fundamental quantities: length, mass, time, electric current, temperature, amount of substance, and luminous intensity. Every other quantity is derived from these.
  • Scalar vs. VectorA scalar quantity has only magnitude, like speed or mass. A vector quantity has both magnitude and direction, like velocity or force.
  • Common SI UnitsThe joule measures energy, the pascal measures pressure, the hertz measures frequency, and the newton second measures momentum and impulse.
  • Astronomical DistancesA light year is the distance light travels in one year. A parsec, about 206,265 astronomical units, is even larger.
  • Dimensional FormulaA quantity’s dimensional formula expresses it in terms of base quantities: mass (M), length (L), and time (T).
📘 Good to Know
Tiny and Vast Scales, Precision Tools
  • Tiny UnitsThe angstrom measures atomic-scale distances; the fermi measures nuclear-scale distances. Both are far smaller than a millimetre.
  • The New KilogramSince 2019, the kilogram has been officially defined using the Planck constant, replacing the old physical metal-cylinder standard kept in France.
  • Precision InstrumentsA vernier calliper and a screw gauge are both precision tools. A screw gauge typically has a finer least count, useful for very small measurements.

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🌟 Great to Know
Dimensional Analysis in Practice
  • The Matching RuleTwo quantities can only be added, or set equal, if their dimensional formulas match exactly. This is a powerful, quick way to catch a wrong physics equation.
  • Dimensionless QuantitiesSome quantities, like strain or relative density, carry no units at all, since they’re built from a ratio of two identical kinds of measurement. Spotting these avoids a common exam trap.
  • Worked ExampleStrain is a change in length divided by an original length: metres divided by metres, leaving nothing behind. Stress, by contrast, is force divided by area, and keeps real physical units.
  • Why It Matters PracticallyPrecision instruments like the vernier calliper and screw gauge matter beyond exams too, since measurement error directly affects real experimental results.
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Exam Point of View

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