Tools and Inquiry — IB Physics skills
T.3.5 Fundamental and Derived Units in Physics — IB Physics HL Revision Notes & Topical Questions
5 min read 8 parts Lesson 10 of 22 1 quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Lesson summary
T.3.5 Fundamental and Derived Units in Physics — IB PHYSICS SL notes: Use SI base units, prefixes and derived units, and convert between common non-SI units.QuantityUnitSymbolLengthmetremMasskilogramkgTimesecondsElectric currentampereATemperaturekelvinKAmount of substancemolemolL…
- Prefixes denote powers of ten
- Mathematical symbols
- Fundamental constants
- Terms in equations
- What the symbols mean
- Circuit symbols
Part 1 of 6Fundamental SI units
| Quantity | Unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric current | ampere | A |
| Temperature | kelvin | K |
| Amount of substance | mole | mol |
| Luminous intensity | candela | cd |
Fundamental SI units
The candela is not used in IB Physics.
The seven base units form the foundation for measuring all quantities.
Part 2 of 6Prefixes
- Prefixes denote powers of ten
- and are listed in the data booklet.
| Prefix | Symbol | Value |
|---|---|---|
| peta | P | 1015 |
| tera | T | 1012 |
| giga | G | 109 |
| mega | M | 106 |
| kilo | k | 103 |
| centi / milli | c / m | 10-2 / 10-3 |
| micro / nano | µ / n | 10-6 / 10-9 |
| pico / femto | p / f | 10-12 / 10-15 |
- Examples
- kW is 103 W, cm is 10-2 m and mg is 10-3 g.
Part 3 of 6Symbols in physics
1Mathematical symbols
- Mathematical symbols e.g. Δ for change in a quantity.
2Fundamental constants
- Fundamental constants e.g. c for the speed of light and h for Planck's constant.
3Terms in equations
- Terms in equations e.g. F = ma.What the symbols mean: F = resultant force (N) · m = mass (kg) · a = acceleration (m s−2)
4Circuit symbols
- Circuit symbols e.g. cell, resistor, voltmeter.
5Nuclear notation
- Nuclear notation in 126C, 12 is the nucleon number, 6 the proton number and C the chemical symbol.
6The same symbol can mean different quantities
- The same symbol can mean different quantities c is speed of light in c = fλ and specific heat capacity in Q = mcΔT.
- P and V stand for pressure and volume in PV = nRT but power and voltage in P = VI.
- In electric fields Ep is potential energy and E is field strength.
Part 4 of 6Derived units
1Every unit can be derived from the seven base units
- Every unit can be derived from the seven base units deduced from the definition of the quantity.
2Newton
- Newton force = mass × acceleration, so N = kg m s-2.
3Joule
- Joule energy = ½ × mass × velocity2, so J = kg m2 s-2.
4Pascal
- Pascal pressure = force / area, so Pa = kg m-1 s-2.
| Derived unit | Quantity | Base units |
|---|---|---|
| newton (N) | force | kg m s-2 |
| pascal (Pa) | pressure | kg m-1 s-2 |
| joule (J) | energy | kg m2 s-2 |
| watt (W) | power | kg m2 s-3 |
| hertz (Hz) | frequency | s-1 |
| coulomb (C) | charge | A s |
| volt (V) | potential difference | kg m2 s-3 A-1 |
| ohm (Ω) | resistance | kg m2 s-3 A-2 |
| tesla (T) | magnetic field strength | kg s-2 A-1 |
| weber (Wb) | magnetic flux | kg m2 s-2 A-1 |
| becquerel (Bq) | radioactivity | s-1 |
Part 5 of 6Common non-SI units
1
radian (rad)
radian (rad) angle where arc length equals radius — π rad = 180°.
2
kilowatt-hour (kW h)
kilowatt-hour (kW h) energy transferred by a 1 kW device in 1 hour — 1 kW h = 3.60 × 106 J.
3
electronvolt (eV)
electronvolt (eV) energy gained by an electron accelerated through 1 V — 1 eV = 1.6 × 10-19 J.
4
eV c-2
eV c-2 unit of mass from E = mc2 — electron rest mass is 0.511 MeV c-2.
5
light-year (ly)
light-year (ly) distance light travels in a year — 1 ly = 9.46 × 1015 m.
6
parsec (pc)
parsec (pc) distance giving a parallax angle of one arcsecond — 1 pc = 3.26 ly.
7
astronomical unit (AU)
Earth–Sun distance — 1 AU = 1.50 × 1011 m.
8
time
- 1 h = 3600 s, 1 day = 8.64 × 104 s, 1 year = 3.15 × 107 s.
Part 6 of 6More from the specification
More from the specification
Percentage uncertainty from graph gradient
- Percentage uncertainty from graph gradient determining percentage uncertainty involves calculating the difference between maximum and minimum gradient slopes on experimental scatter graphs.
Significant figures in measured quantities
- Significant figures in measured quantities calculated values must be quoted to consistent significant figures matching the lowest precision among experimental input quantities.
Vector resolution and resultant magnitude
- Vector resolution and resultant magnitude vector addition combines orthogonal component vectors to calculate resultant displacement magnitude and directional angles using trigonometry.
Fundamental SI Units vs Derived Physical Quantities
- The International System of Units (SI) defines seven fundamental base units; all other physical quantities are derived by multiplying or dividing base units (e.g. 1 N = 1 kg·m·s⁻², 1 J = 1 kg·m²·s⁻²).
- (metre, kilogram, second, ampere, kelvin, mole, candela)
Scalar vs Vector Quantities and Vector Addition
- A scalar quantity possesses only magnitude (such as mass, time,
- or energy),
- whereas a vector quantity possesses both magnitude and direction (such as displacement, velocity,
- or force); vectors are resolved into orthogonal components or added vectorially to determine the resultant.
Experimental Uncertainties, Significant Figures, and Graphs
- Experimental measurements carry uncertainty; percentage uncertainty is calculated as × 100%,
- (Absolute Uncertainty / Mean Value)
- and results should be quoted to appropriate significant figures; plotting data on linear graphs allows determination of physical constants from the gradient.
Percentage uncertainty
- The absolute uncertainty divided by the value, times 100%.
Absolute uncertainty
- The range ±Δx in the same unit as the measurement.
Percentage error
- Difference from the accepted value as a percentage of it.
Percentage difference
- Difference divided by accepted value × 100
Scale drawing
- Accurate drawing with a chosen scale.
Parallelogram method
- Vector addition using a parallelogram of vectors.
Uncertainty
- An estimate of the range in which the true value is expected to lie.
Vector
- Quantity with magnitude and direction.
Gradient
- Slope of a graph line.
Variable
- A factor that can change in an investigation.
Displacement
- Change in position.
Proportional
- Changing by the same factor as another quantity.
Scalar
- Quantity with magnitude only.
Significant figures
- Digits carrying meaningful information in a number.
a
− ω2x
What the symbols mean: a = acceleration (m s−2) · ω = angular frequency (rad s−1) · x = displacement from equilibrium (m); the minus sign means a always points back to the centre
Key terms
| Term | Meaning |
|---|---|
| SI base unit | One of seven fundamental units such as metre, kilogram and second. |
| Derived unit | Unit built from base units, such as the newton. |
| Prefix | Multiplier of ten placed before a unit. |
| Electronvolt | Energy gained by an electron through 1 V; 1.6 × 10-19 J. |
| Kilowatt-hour | Energy of a 1 kW device in one hour; 3.60 × 106 J. |
| Parsec | Distance with a parallax of one arcsecond; 3.26 ly. |
Avoid these mistakes
1
Using grams in a formula that needs kilograms — convert to the base unit.
2
Mixing up prefixes such as milli (10-3 and micro (10-6.
3
Forgetting that a derived unit expressed in base units must match on both sides of an equation.
4
Using the same symbol for different quantities — check the context (c, P, V, E).
5
Treating the electronvolt as a unit of voltage — it is a unit of energy.
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