Units, Measurement, and Estimation
Why Measurement Matters
Core idea
Applied physics starts with reliable measurement. Every model, experiment, and engineering decision depends on identifying the relevant quantities, their units, and the uncertainty attached to them.
A useful habit
Always write units at every step. If the units do not match, the physics is probably wrong.
SI Units and Derived Quantities
Common quantities
Dimensional analysis
Dimensional analysis checks whether an equation is physically meaningful. For example, if , then because and . This method can also help you derive relationships before doing a full derivation.
Which quantity has units of ?
Force is measured in newtons, and .
Correct answer: Force
What does dimensional analysis help verify?
It checks whether both sides of an equation have matching dimensions and can also suggest possible functional forms.
Correct answer: Whether an equation is physically consistent
Uncertainty and Significant Figures
Measurement error
No measurement is exact. Random error produces scatter, while systematic error shifts results in one direction. Reporting uncertainty tells others how much confidence to place in the value.
Types of uncertainty
| Type | Typical cause |
|---|---|
| Random | Fluctuations in instrument readings |
| Systematic | Miscalibration or biased method |
| Resolution | Smallest readable increment |
| Human | Parallax or reaction time |
A scale reads mass as . The last digit is uncertain because of what?
The last reported digit reflects the instrument’s resolution and estimated reading uncertainty.
Correct answer: Instrument resolution
Why is order-of-magnitude estimation useful in applied physics?
Estimates help catch unrealistic answers and guide design decisions when exact calculations are unnecessary.
Correct answer: It gives a quick plausibility check