A-Level IAL Unit 1 01 Quantities SI Units

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Unit 1 01 Physical Quantities and SI Units

1. Learning Objectives

  • Subject Content:
    • Recall the seven base quantities and their SI units.
    • Understand how to derive units for other physical quantities.
    • Memorize and apply standard prefixes (pico to tera).
  • Language Goals:
    • Master the terminology for “Base Units” and “Derived Units”.
    • Accurately describe the relationship between units using “in terms of”.

2. Key Terminology

Term Notes
Physical Quantity Numerical value + Unit
Base Quantity The 7 fundamental quantities
SI Base Units Système International d’Unités
Derived Units Units created from base units
Homogeneity Units on both sides must match
Prefixes e.g., Kilo-, Mega-, Micro-
Scalar / Vector Magnitude vs. Direction

3. The 7 SI Base Units

In A-level Physics, every unit you encounter can be broken down into these seven pillars:

Base Quantity Symbol SI Base Unit Unit Abbreviation
Length meter m
Mass kilogram kg
Time second s
Electric Current ampere A
Temperature kelvin K
Amount of Substance mole mol
Luminous Intensity candela cd
Note

In A-level exams, Candela (cd) rarely appears; focus on the first six.

4. Derived Units

Derived units are products or quotients of base units.

They are obtained by multiplying or dividing base units through physical formulas.

Derived Quantity Unit Name Symbol In Base Units
Force Newton N
Pressure Pascal Pa
Energy/Work Joule J
Power Watt W
Frequency Hertz Hz
Charge Coulomb C
Potential Diff. Volt V
Note

Based on the table provided, these Derived Units are primarily deduced through the following fundamental physical definition formulas. For clarity, I will map them to the derivation process of the base units:

1. Mechanics

  • Force – Newton (N)
    • Physical Formula: Newton’s Second Law
    • Unit Derivation:
  • Pressure – Pascal (Pa)
    • Physical Formula: Definition of Pressure
    • Unit Derivation:
  • Energy/Work – Joule (J)
    • Physical Formula: Definition of Work
      (Can also be derived using the kinetic energy formula )
    • Unit Derivation:
  • Power – Watt (W)
    • Physical Formula: Definition of Power
    • Unit Derivation:

2. Waves/Periodic Motion

  • Frequency – Hertz (Hz)
    • Physical Formula: Frequency-Period Relation
    • Unit Derivation:

3. Electricity

  • Charge – Coulomb (C)
    • Physical Formula: Definition of Current
    • Unit Derivation:
    • (Note: Ampere A is a base unit, Coulomb C is a derived unit)
  • Potential Diff. (Voltage) – Volt (V)
    • Physical Formula: Definition of Potential Difference (Work done per unit charge) or Electrical Power formula
    • Unit Derivation (Using ):

Summary

You can see a clear hierarchical relationship:

  1. Foundation:
  2. First-level Derived: (), (), ()
  3. Second-level Derived: (), ()
  4. Third-level Derived: (), ()

5. Standard Prefixes

Prefix Symbol Multiplier Meaning
Tera T Trillion
Giga G Billion
Mega M Million
Kilo k Thousand
Deci d Tenth
Centi c Hundredth
Milli m Thousandth
Micro Millionth
Nano n Billionth
Pico p Trillionth

6. Practice Exercises

Instructions: Express the following units strictly in terms of SI Base Units. Show your working using the relevant physical formulas.

Q1. The unit of Pressure is the Pascal (Pa). Using the formula , derive the SI base units of the Pascal.

Q2. The Kinetic Energy () of an object is given by . Show that the SI base units for energy are .

Q3. The Resistivity () of a wire is given by the formula , where is resistance, is cross-sectional area, and is length. Derive the SI base units of resistivity.

(Hint: Use and to find the units of first).

Q4. A student claims that the period of a simple pendulum is given by , where is length and is acceleration of free fall. Use units to check if this equation is homogeneously correct.

Q5. Convert the following values into standard SI units (without prefixes) using scientific notation:

  • (a)
  • (b)
  • (c)

This standard Mark Scheme utilizes the step-by-step derivation method common in A-level exams.

Answers

Q1. SI Base Units of Pressure (Pa)

  • Formula:
  • Step 1: Force , so the units of are (Newton).
  • Step 2: Area has units of .
  • Step 3: Substitute into the pressure formula:
  • Final Answer:

Q2. SI Base Units of Energy (J)

  • Formula:
  • Step 1: Identify units of each term (Note: is a dimensionless constant).
    • (mass) =
    • (velocity) =
  • Step 2: Square the velocity units: .
  • Step 3: Multiply by mass:
  • Final Answer:

Q3. SI Base Units of Resistivity ()

  • Formula:
  • Step 1: Find units of Resistance .
    • From .
    • From .
    • Units of Power () = (from ).
    • Units of .
    • Units of .
  • Step 2: Substitute back into formula.
  • Final Answer:

Q4. Homogeneity Check (Period of Pendulum)

  • Equation:
  • Left Hand Side (LHS): is time, so unit is s.
  • Right Hand Side (RHS):
    • is a constant (no units).
    • is length: m.
    • is acceleration: .
    • Units of .
    • Units of .
  • Conclusion: Since LHS units = RHS units (s = s), the equation is homogeneously correct.

Q5. Prefix Conversion

  • (a) :


  • (b) :


  • (c) :
    • , and we must convert to the base unit kg (not gram!).
    • .
    • .