🍏Principles of Physics I Unit 1 Review

Physics is built on measurement. To describe anything quantitatively, you need agreed-upon units, and you need to understand how reliable your measurements are. This section covers the SI unit system, how to convert between units, and how to handle precision and accuracy.

Fundamental and Derived SI Units

The SI system (Système International) defines seven fundamental units. Every other unit in physics can be built from combinations of these seven.

Quantity	Unit	Symbol	Definition
Length	meter	m	Distance light travels in vacuum in $\frac{1}{299{,}792{,}458}$ of a second
Mass	kilogram	kg	Defined via the Planck constant ( $6.62607015 \times 10^{-34} \text{ J·s}$ )
Time	second	s	Duration of 9,192,631,770 radiation periods of a cesium-133 atom
Electric current	ampere	A	Flow of $\frac{1}{1.602176634 \times 10^{-19}}$ elementary charges per second
Temperature	kelvin	K	Defined via the Boltzmann constant, with 0 K at absolute zero
Amount of substance	mole	mol	Exactly $6.02214076 \times 10^{23}$ entities (Avogadro's number)
Luminous intensity	candela	cd	Luminous intensity in a given direction

Derived units are combinations of fundamental units. For this course, the most important ones are:

Newton (N): The unit of force. $1 \text{ N} = 1 \text{ kg} \cdot \text{m/s}^2$
Joule (J): The unit of energy or work. $1 \text{ J} = 1 \text{ N} \cdot \text{m}$
Watt (W): The unit of power (energy per time). $1 \text{ W} = 1 \text{ J/s}$
Pascal (Pa): The unit of pressure. $1 \text{ Pa} = 1 \text{ N/m}^2$

SI prefixes let you express very large or very small quantities without writing out all those zeros:

Prefix	Symbol	Factor	Example
Giga	G	$10^9$	1 GHz = $10^9$ Hz
Mega	M	$10^6$	1 MW = $10^6$ W
Kilo	k	$10^3$	1 km = $10^3$ m
Milli	m	$10^{-3}$	1 mm = $10^{-3}$ m
Micro	μ	$10^{-6}$	1 μg = $10^{-6}$ g
Nano	n	$10^{-9}$	1 ns = $10^{-9}$ s

Fundamental and derived SI units, Appendix 1: Units of Measurement, Mathematical Rules, and Conversion Factors – Physical ...

Unit Conversion Techniques

Unit conversion is something you'll do constantly in physics. The core idea is multiplying by a conversion factor that equals 1, so you change the units without changing the value.

For example, to convert 5.0 km to meters:

$5.0 \text{ km} \times \frac{1000 \text{ m}}{1 \text{ km}} = 5000 \text{ m}$

The fraction $\frac{1000 \text{ m}}{1 \text{ km}}$ equals 1, so you're just rewriting the same distance in different units. Always set up the fraction so the unit you want to cancel appears in the denominator.

Common conversions to know:

Length: 1 in = 2.54 cm (exact), 1 mi ≈ 1.609 km, 1 m = 100 cm
Mass: 1 kg = 1000 g, 1 lb ≈ 0.4536 kg
Time: 1 min = 60 s, 1 hr = 3600 s, 1 day = 86,400 s

Temperature conversions use formulas rather than simple ratios because the scales have different zero points:

Celsius to Fahrenheit: $°F = °C \times \frac{9}{5} + 32$
Celsius to Kelvin: $K = °C + 273.15$
Fahrenheit to Celsius: $°C = (°F - 32) \times \frac{5}{9}$

Kelvin is the SI unit for temperature. It starts at absolute zero (the coldest possible temperature), which makes it natural for physics equations.

Fundamental and derived SI units, Units | Boundless Physics

Precision and Accuracy in Measurements

These two words mean different things in physics, and mixing them up is a common mistake.

Precision is how consistent your measurements are when you repeat them. Think of throwing darts: if they all land close together (even if they're far from the bullseye), that's high precision. Precision depends on your instrument. A ruler marked in millimeters is more precise than one marked only in centimeters.
Accuracy is how close your measurement is to the true value. If those tightly-grouped darts are also near the bullseye, you have high accuracy. Poor accuracy often comes from systematic errors, like using a scale that's slightly miscalibrated.

You can have high precision but low accuracy (consistently wrong), or high accuracy but low precision (scattered around the right answer). The goal is both.

Significant figures tell you how much certainty a measurement carries. The rules:

All non-zero digits are significant: 123 has 3 sig figs
Zeros between non-zero digits are significant: 1002 has 4 sig figs
Leading zeros are not significant: 0.00123 has 3 sig figs
Trailing zeros after a decimal point are significant: 1.2300 has 5 sig figs

When doing calculations, your answer can't be more precise than your least precise input:

Addition/subtraction: Round to the fewest decimal places among your inputs
Multiplication/division: Round to the fewest significant figures among your inputs

Dimensional Analysis Applications

Dimensional analysis is a powerful tool for checking your work. Every physical quantity can be expressed in terms of three fundamental dimensions for mechanics:

[L] for length
[M] for mass
[T] for time

Derived quantities are combinations of these. Velocity has dimensions $[LT^{-1}]$ , and force has dimensions $[MLT^{-2}]$ .

The key rule: both sides of any valid physics equation must have the same dimensions. If they don't, something is wrong.

How to use dimensional analysis to check an equation:

Write out the dimensions of every quantity in the equation
Express any derived quantities in terms of $[M]$ , $[L]$ , and $[T]$
Simplify each side and confirm the dimensions match

For example, does $v = at$ make sense dimensionally? The left side is velocity: $[LT^{-1}]$ . The right side is acceleration times time: $[LT^{-2}] \times [T] = [LT^{-1}]$ . They match, so the equation is at least dimensionally valid.

You can also use dimensional analysis to figure out relationships between quantities. If you know a result depends on certain variables, you can combine them so the dimensions work out. This won't give you numerical constants (like $\frac{1}{2}$ ), but it will give you the correct structure of the equation. This technique shows up in more advanced topics like fluid dynamics and scaling laws.

🍏Principles of Physics I Unit 1 Review