Ch 1 · 1 Physical Quantities and Units · A Level Physics 9702
Topic 1 of 3 in Physical Quantities, Kinematics and Dynamics — A Level Physics 9702 — 49 lessons.
Introduction
Every result in physics is a number and a unit, and every measurement has some uncertainty. This first topic gives you the tools you will use in every other topic: SI units, checking equations, handling uncertainties and working with vectors. (Syllabus topic 1: sections 1.1–1.4.)
Key ideas — 1.1 Physical quantities and estimates
A physical quantity has a numerical magnitude and a unit: "the length is 2.5 m". A number without a unit ("2.5") is meaningless.
🧑🏫 Teacher's explanation
Imagine you are telling a friend how far you ran. If you say "I ran 5," they won't know if you mean 5 meters, 5 kilometers, or 5 light-years. A physical quantity is like a complete sentence: it needs a number (the magnitude) and a label (the unit) to actually mean something in the real world. Without the unit, the number is just an abstract concept.
📖 Definitions
🔍 Worked example — Easy
A student measures the length of a rod as 15.4 cm. Express this length in meters using standard scientific notation.
🔍 Worked example — Standard
A measurement of time has an absolute uncertainty of Δ t = 0.02 s. If the measured time is t = 0.50 s, calculate the percentage uncertainty in the time.
🔍 Worked example — Exam-style
Check the homogeneity of the equation for kinetic energy: E_k = 1/2mv^2, where E_k is energy, m is mass, and v is velocity. Express the units of E_k in SI base units.
⚠️ Common errors
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🎯 Exam question
Key ideas — 1.2 SI units
SI base quantities you must recall:
🧑🏫 Teacher's explanation
Think of SI units as the 'DNA' of physics. Just as every living thing is built from a specific set of chemical elements, every physical measurement is built from a core set of base quantities. When we combine these, we get 'derived units' like Newtons or Joules. If you try to build a molecule with the wrong atoms, it won't work; similarly, if an equation's units don't match on both sides, the physics is fundamentally broken.
📖 Definitions
🔍 Worked example — Easy
Express the unit of pressure, the Pascal (Pa), in terms of SI base units.
🔍 Worked example — Standard
A student measures the mass of an object as 250 g and its volume as 50 cm^3. Calculate the density in kg m^-3.
🔍 Worked example — Exam-style
Check the homogeneity of the equation E = mc^2, where E is energy, m is mass, and c is the speed of light.
⚠️ Common errors
🧠 Quick check 1
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🎯 Exam question
(a) Determine the SI base units of the constant k. (b) A student measures x = 2.0 cm and F = 10 N. Calculate the value of k in N m^-1. [3 marks]
Key ideas — 1.3 Errors and uncertainties
Systematic errors shift every reading by the same amount in the same direction. Causes: a zero error (a meter that does not read zero when it should), an incorrectly calibrated instrument, or a consistent technique fault such as parallax from the same angle every time. They cannot be reduced by repeating and averaging; correct them by checking the zero, recalibrating, or improving the method.
🧑🏫 Teacher's explanation
Imagine you are playing darts. If all your darts land in a tight cluster in the top-left corner of the board, you are being precise (consistent) but not accurate (you missed the bullseye). If your darts are scattered all over the board, you are neither precise nor accurate. If they are all clustered right around the bullseye, you are both.
📖 Definitions
🔍 Worked example — Easy
A student measures the length of a rod as L = (25.0 ± 0.2) cm and the width as W = (10.0 ± 0.1) cm. Calculate the uncertainty in the area A.
🔍 Worked example — Standard
A mass is measured as m = (5.00 ± 0.05) kg. Calculate the uncertainty in the weight W of the mass, given g = 9.81 m/s^2 (assume g has no uncertainty).
🔍 Worked example — Exam-style
The radius of a sphere is measured as r = (2.0 ± 0.1) cm. Calculate the percentage uncertainty in the volume V of the sphere.
⚠️ Common errors
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🎯 Exam question
Key ideas — 1.4 Scalars and vectors
A scalar has magnitude only: distance, speed, mass, time, energy, power, temperature, charge, pressure, density.
🧑🏫 Teacher's explanation
Imagine you are walking across a large, open field. If I tell you, "Walk 10 meters," you don't know where you'll end up; you only know how much effort you spent. This is a scalar quantity—it only cares about 'how much'. However, if I tell you, "Walk 10 meters North," I have given you a vector quantity. You now have both a magnitude (10m) and a direction (North).
📖 Definitions
🔍 Worked example — Easy
A hiker walks 5.0 km East and then 12.0 km North. Calculate the magnitude of the hiker's total displacement.
🔍 Worked example — Standard
A force of 50.0 N is applied at an angle of 30.0^° to the horizontal. Calculate the vertical component of this force.
🔍 Worked example — Exam-style
A boat travels at 4.00 m/s due North. The river current flows at 3.00 m/s due East. Calculate the magnitude of the resultant velocity of the boat relative to the shore.
⚠️ Common errors
🧠 Quick check 1
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🎯 Exam question
Worked example
Example 1: base units. Show that the unit of power, the watt, is kg m² s⁻³.
🔍 Worked example — Easy
Show that the unit of power, the watt (W), is equivalent to kg m^2 s^-3 using base units.
🔍 Worked example — Standard
A wire has a diameter d = 0.50 ± 0.01 mm and a length L = 1.000 ± 0.002 m. Calculate the percentage uncertainty in the volume V = π d^2/4 L.
🔍 Worked example — Exam-style
A boat travels due North at 4.0 m s^-1 across a river flowing due East at 3.0 m s^-1. Calculate the magnitude and direction of the resultant velocity.
⚠️ Common errors
Common mistakes
Practice
Answers: (1) kg m² s⁻². (2) Each term has units m² s⁻²: [v^2] = [u^2] = m^2s^-2, [as] = m s^-2 × m. (3) Accuracy: closeness to the true value; precision: closeness of repeated readings to each other. (4) R = 12.0/2.4 = 5.0\ Omega; % uncertainty = 0.2/12.0 + 0.1/2.4 = 1.7\% + 4.2\% = 5.9\%; Δ R = 0.3\ Omega; R = 5.0 ± 0.3\ Omega. (5) 80cos 60° = 40 N horizontal; 80sin 60° = 69 N vertical. (6) tfrac12 × 70 × 10^2 ≈ 3500 J, of order 10^3–10^4 J.