Welcome to the World of Physics!
Welcome to your first chapter of AS Level Physics! Physics is often called the "fundamental science" because it tries to explain how everything in the universe works—from the tiniest particles inside an atom to the giant galaxies in space. In this first chapter, we are going to learn how physicists measure the world. Don't worry if some of this seems like a lot of detail; once you get the hang of these "rules of the game," the rest of Physics becomes much easier to understand!
1.1 Physical Quantities
In Physics, a physical quantity is anything that can be measured. Every time you write down a measurement, it must have two parts: a numerical magnitude (the number) and a unit.
Example: If you say a table is "1.5" long, no one knows what you mean. Is it 1.5 centimeters? 1.5 meters? 1.5 kilometers? You must say 1.5 m.
Making Estimates
Sometimes in Physics, we don't need a perfect measurement, but we do need a "ballpark figure." Being able to estimate is a key skill. Here are some common estimates you should know for your exams:
• Mass of an adult: 70 kg
• Height of an adult: 1.7 m
• Mass of an apple: 100 g (0.1 kg)
• Speed of sound in air: 330 \(m s^{-1}\)
• Weight of an apple: 1 N
Quick Review: A physical quantity = Number + Unit. If you forget the unit in an exam, you lose the mark!
1.2 SI Units
To make sure scientists all over the world understand each other, we use the SI system (International System of Units). Think of this as the "universal language" of science.
The 5 Base Quantities
You need to memorize these five base quantities and their units:
1. Mass: kilogram (kg)
2. Length: meter (m)
3. Time: second (s)
4. Electric Current: ampere (A)
5. Temperature: kelvin (K)
Derived Units
Most other units are "made" by combining these base units. These are called derived units. For example, Speed is Distance divided by Time. In units, that is \(m\) divided by \(s\), written as \(m s^{-1}\).
Did you know? Even the Newton (N) for force is a derived unit! Since \(Force = mass \times acceleration\), the units are \(kg \times m s^{-2}\). So, \(1 N = 1 kg m s^{-2}\).
Homogeneity: The "Units Must Match" Rule
An equation is homogeneous if the units on the left side are exactly the same as the units on the right side. If they don't match, the equation is definitely wrong!
Example: In the equation \(v = u + at\), the units for \(v\) are \(m s^{-1}\). The units for \(u\) are \(m s^{-1}\). The units for \(at\) are \((m s^{-2} \times s) = m s^{-1}\). Everything matches!
Unit Prefixes
Prefixes are handy short-cuts for very large or very small numbers. You need to know these:
Large Multiples:
• Tera (T): \(10^{12}\)
• Giga (G): \(10^9\)
• Mega (M): \(10^6\)
• Kilo (k): \(10^3\)
Small Submultiples:
• Deci (d): \(10^{-1}\)
• Centi (c): \(10^{-2}\)
• Milli (m): \(10^{-3}\)
• Micro (\(\mu\)): \(10^{-6}\)
• Nano (n): \(10^{-9}\)
• Pico (p): \(10^{-12}\)
Key Takeaway: Always convert your units back to the "base" (like grams to kilograms) before doing calculations!
1.3 Errors and Uncertainties
In the real world, no measurement is perfect. We use the terms "error" and "uncertainty" to describe these imperfections.
Systematic vs. Random Errors
Systematic Errors: These happen because of a problem with the equipment or the setup. They shift all your readings by the same amount in the same direction.
Example: A "Zero Error" where a scale shows 0.1g even when nothing is on it.
How to fix: Calibrate the equipment or subtract the error from your results.
Random Errors: These are unpredictable. They make your readings scatter around the true value.
Example: Human reaction time when using a stopwatch.
How to fix: Take many readings and calculate an average.
Accuracy vs. Precision
Imagine you are playing darts:
• Accuracy: How close your darts are to the bullseye (the true value).
• Precision: How close your darts are to each other (the consistency of your results).
Combining Uncertainties
When you use measurements to calculate something else, the uncertainty "adds up."
1. Adding or Subtracting: Add the absolute uncertainties.
\( (A \pm \Delta A) + (B \pm \Delta B) \rightarrow \text{Total Uncertainty} = \Delta A + \Delta B \)
2. Multiplying or Dividing: Add the percentage uncertainties.
\( \% \text{Uncertainty in } Z = \% \text{Uncertainty in } A + \% \text{Uncertainty in } B \)
Common Mistake: Students often try to subtract uncertainties when subtracting numbers. Never subtract uncertainties! They always make the result less certain, so they always add up.
1.4 Scalars and Vectors
This is one of the most important concepts in Physics. Every quantity is either a scalar or a vector.
The Difference
• Scalar: Has magnitude (size) only. Examples: mass, time, temperature, energy, distance, speed.
• Vector: Has magnitude AND direction. Examples: force, velocity, acceleration, displacement, momentum.
Adding Vectors
You can't just add vectors like normal numbers if they are pointing in different directions. We use the "tip-to-tail" method.
1. Draw the first vector as an arrow.
2. Start the second vector's "tail" at the "tip" of the first one.
3. The resultant is the arrow drawn from the very start to the very end.
Resolving Vectors (Splitting them up)
Sometimes it is easier to split a diagonal vector into two parts: a horizontal component and a vertical component. If you have a vector \(V\) at an angle \(\theta\) to the horizontal:
• Horizontal component (\(V_x\)): \(V \cos \theta\)
• Vertical component (\(V_y\)): \(V \sin \theta\)
Memory Aid: "Cos is across" (the horizontal part across the angle). "Sin is the other one."
Quick Review:
• Scalars = Size only.
• Vectors = Size + Direction.
• Use \(V \cos \theta\) for the side adjacent to the angle.
End of Chapter Summary
You’ve now covered the basics of how we measure the universe! You know that units are vital, that all measurements have some uncertainty, and that direction matters for vectors. Don't worry if resolving vectors feels tricky at first—practice makes perfect. Keep these notes handy as you move on to Kinematics, as you will use these skills in every single chapter that follows!