SI units and prefixes
Section: Physical Quantities and Units | Syllabus: Cambridge AS Level Physics 9702
Base Units These are the fundamental units of measurement that are used to define all other units and can't be broken down into simpler units . The International System of Units (SI) defines seven base quantities.
At AS Level, you need to recall the following five: Base Quantity SI Base Unit Symbol Length metre m Mass kilogram kg Time second s Electric Current ampere A Thermodynamic Temperature kelvin K Note The Kelvin scale starts at absolute zero (0 K).
K = °C + 273.15. Derived Units Derived units are units that can be expressed as combinations of the five SI base units (metre, kilogram, second, ampere, and kelvin). They are obtained by multiplying or dividing these base units.
Most physical quantities have derived units . These are units which can be expressed in terms of the five SI base units (m, kg, s, A, K). Quantity Derived Unit In SI Base Units Force Newton (N) kg m s^-2 Pressure Pascal (Pa) kg m^-1 s^-2 Energy / Work Joule (J) kg m^2 s^-2 Power Watt (W) kg m^2 s^-3 Frequency Hertz (Hz) s^-1 Charge Coulomb (C) A s Potential Diff Volt (V) kg m^2 s^-3 A^-1 Example: Derived Units Question: Express the newton, N, in terms of base SI units.
Answer Use the equation F = ma In this equation F is force, m is mass and a is acceleration The unit of mass is kg and the unit of acceleration is m s^-2 Therefore unit of F = kg m s^-2 The newton, N, expressed in base SI units is kg m s^-2 Example: Deriving the Volt Voltage = Work done / Charge V = J / C Base units for J: kg m^2 s^-2 Base units for C: A s Base units for V: (kg m^2 s^-2) / (A s) = kg m^2 s^-3 A^-1 Checking Homogeneity An equation is homogeneous if the SI base units on both sides are the same.
This is a powerful tool to check if an equation is physically possible. Worked Example 1 One of the equations of motion is v^2 = u^2 + 2as where v and u are velocities, 2 is a constant, a is acceleration and s is displacement.
Use base SI units to prove the homogeneity of this equation. Answer List the units for each quantity: v is in m s^-1 so v^2 is in m^2 s^-2 u is in m s^-1 so u^2 is in m^2 s^-2 2 is a constant, so no unit a is in m s^-2 s is in m Substitute these into the equation: m^2 s^-2 = m^2 s^-2 + (m s^-2) × (m) m^2 s^-2 = m^2 s^-2 + m^2 s^-2 All terms have the same units (m^2 s^-2), which proves its homogeneity.
Worked Example 2 Use base SI units to prove the homogeneity of the following equation: v = u + at where v and u are velocities, a is acceleration and t is time. Answer Units of v: m s^-1 Units of u: m s^-1 Units of at: (m s^-2) × s = m s^-1 Since all terms have the same base units (m s^-1), the equation is homogeneous.
Pro Tip Numbers (like fraction in fractionmv^2 or 2 in 2as) have no units and are ignored when checking homogeneity. When adding or subtracting terms with the same units, the result keeps those units.
For example, if an equation shows m^2s^-2 = m^2s^-2 + m^2s^-2, this is still homogeneous-both sides have units of m^2s^-2. Prefixes Scientific notation and prefixes are used to express very large or very small quantities conveniently.
Prefix Symbol Factor Tera T 10^12 Giga G 10^9 Mega M 10^6 Kilo k 10^3 Deci d 10^-1 Centi c 10^-2 Milli m 10^-3 Micro μ 10^-6 Nano n 10^-9 Pico p 10^-12
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