Unit 1: Units and Measurement
How physics measures, converts, and estimates the world before a single equation of motion shows up.
5 topics · 18 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
The Scope of Physics and Orders of Magnitude
- How it worksHow do physicists use powers of ten to compare the size of an atom with the size of a galaxy?
- Worked exampleFind the order of magnitude of the number of atoms in a 1 kg block of iron with molar mass 56 g/mol.
- Common mistakeWhy isn't an estimate that's off by a factor of 3 considered a failed calculation in physics?
- Going furtherWhat happens to a physical law's usefulness when you push it far outside the scale it was tested at?
Your turn1 of 2
A block of a substance with molar mass M (g/mol) has mass m (grams). Using Avogadro's number NA, write an expression, in terms of m, M, and NA, for the number of atoms it contains.Units and the SI System
- How it worksHow do the seven SI base units combine to build every other unit used in physics?
- Common mistakeWhy isn't a kilogram actually a unit of weight?
- Going furtherWhat happens to a formula's credibility if you check its units and they don't come out matching?
Your turn1 of 2
The newton is built from the SI base units of mass, length, and time. Write an expression, in terms of m and a, for the force needed to give an object of mass m an acceleration a.Unit Conversion
- How it worksHow do conversion factors let you cancel units like fractions to switch between measurement systems?
- Worked exampleFind the speed in meters per second of a car going 90 km/h.
- Worked exampleFind the density in kilograms per cubic meter of a material with density 1.2 g/cm3.
- Common mistakeWhy doesn't multiplying by a conversion factor ever change the actual quantity you're measuring?
Your turn1 of 2
A car travels at 103 km/h. What is its speed in meters per second?Dimensional Analysis
- How it worksHow do you track length, mass, and time through both sides of an equation to check it's consistent?
- Worked exampleFind out whether the guessed formula T = 2 π √(L/g) survives a dimensional-analysis check.
- Common mistakeWhy doesn't dimensional analysis alone tell you whether a formula's numerical constant is correct?
- Going furtherWhat happens when you use dimensional analysis to guess the form of a formula you can't quite remember?
Your turn1 of 2
A pendulum of length 1.86 m is claimed to have period T = 2 π √(L/g), with g = 9.8 m/s2. What period, in seconds, does this formula predict?Estimation and Fermi Problems
- How it worksHow do you break an impossible-sounding question into pieces you can each guess within a factor of ten?
- Worked exampleFind the number of piano tuners in a city of 5 million people using a Fermi estimate.
- Going furtherWhat happens to the accuracy of a Fermi estimate as you chain more uncertain factors together?
Your turn1 of 2
Estimate the number of piano tuners in a city of 7 million people, assuming 1 household in 20 owns a piano, an average of 3 people per household, each piano is tuned once a year, and one tuner can service 500 pianos a year.