Mechanics · Quick Reference

Physical Quantities Cheat Sheet

Mechanics · Lesson 1/19

In one line: a physical quantity is anything that can be measured — physics begins by carefully defining what we measure and how, before any equations come into play.

Key Ideas

1Physical Quantity. Any property of an object or system that can be measured and expressed with a number and a unit, like mass, length, or time.

2Fundamental (Base) Quantities. The small set of independent quantities from which all others are derived: length, mass, time, electric current, temperature, amount of substance, and luminous intensity.

3Derived Quantities. Quantities built by combining base quantities, such as speed (length/time) or force (mass x length/time^2).

4Magnitude and Unit. A complete measurement always needs both a number (magnitude) and a unit -- '5' alone is meaningless without knowing '5 meters' or '5 seconds'.

5Dimensional Analysis. Checking that both sides of an equation have matching combinations of base quantities (dimensions), a useful way to catch errors in physics formulas.

Worked Examples

Classify 'mass' as a fundamental or derived quantity.

Fundamental quantity

Classify 'speed' as a fundamental or derived quantity.

Derived quantity (length/time)

Why is '10' not a complete physical measurement on its own?

Because it is missing a unit, so its meaning is undefined

Practice Yourself

Is 'time' a fundamental or derived quantity?

Fundamental

Is 'force' a fundamental or derived quantity?

Derived

Is 'temperature' a fundamental or derived quantity?

Fundamental

What two things does a complete physical measurement always need?

A magnitude (number) and a unit