Welcome to the Language of Physics!
Welcome to your first step in OCR AS Level Physics! Before we can calculate the speed of a galaxy or the charge of an electron, we need to speak the same language. In Physics, that language is Physical Quantities and Units. Think of this chapter as the "ruler" we use to measure the universe. By the end of these notes, you'll know how to break down any measurement into its simplest form and how to spot a "fake" equation just by looking at its units.
Don't worry if some of the math looks a bit strange at first—once you see the patterns, it becomes a very handy puzzle!
1. What is a Physical Quantity?
In Physics, everything we measure is called a physical quantity. A quantity isn't just a number; it must tell us "how much" and "of what."
Every physical quantity consists of two parts:
1. A numerical value (the number).
2. A unit (the standard of measurement).
Example: If you say a car is "50" fast, that means nothing! Is it 50 miles per hour? 50 meters per second? 50 centimeters per year? To make sense, you must say 50 m s\(^{-1}\). Here, 50 is the numerical value and m s\(^{-1}\) is the unit.
Quick Review: The Recipe Analogy
Imagine a recipe that says "Add 5 flour." You'd be confused! You need to know if it's 5 grams, 5 cups, or 5 kilograms. Physics is exactly the same—the unit gives the number its meaning.
Key Takeaway:
Physical Quantity = Numerical Value \(\times\) Unit
2. The S.I. Base Units
To keep scientists across the world on the same page, we use the Système Internationale (S.I.). There are six base quantities you need to know for this course. Every other unit in Physics is built from these "building blocks."
The "Big Six" Base Units:
- Mass: kilogram (kg)
- Length: metre (m)
- Time: second (s)
- Current: ampere (A)
- Temperature: kelvin (K)
- Amount of substance: mole (mol)
Memory Aid (Mnemonic):
Try this to remember them: Many Lions Take Constant Terrible Aps.
(Mass, Length, Time, Current, Temperature, Amount)
Did you know? We use Kelvin (K) for temperature because it starts at "Absolute Zero," where particles stop moving entirely. To turn Celsius (\(^{\circ}\)C) into Kelvin, just add 273.15!
Key Takeaway:
Memorize these six! They are the foundation for everything else in your AS Level course.
3. Derived Units
Most quantities we use, like Speed, Force, or Energy, are derived units. This means they are combinations of the base units.
How to find a Derived Unit in Base Units:
1. Write down the formula for the quantity.
2. Replace the symbols with their units.
3. Cancel or combine them.
Example 1: Density (\(\rho\))
Formula: \(\rho = \frac{m}{V}\) (Mass divided by Volume)
Units: \(\frac{\text{kg}}{\text{m}^3}\)
S.I. Base Units: kg m\(^{-3}\)
Example 2: Momentum (p)
Formula: \(p = mv\) (Mass \(\times\) Velocity)
Units: \(\text{kg} \times \text{m s}^{-1}\)
S.I. Base Units: kg m s\(^{-1}\)
Step-by-step Tip: Whenever you see a division sign in a unit, like \(\text{m}/\text{s}\), we write it as \(\text{m s}^{-1}\) in Physics. It looks more professional and is easier to use in calculations!
4. Homogeneity: The Ultimate Equation Check
A "homogeneous" equation is just a fancy way of saying an equation is balanced. For an equation to be physically possible, the units on the left side must be the same as the units on the right side.
Why is this useful?
If you're in an exam and can't remember if a formula is \(v = at\) or \(v = at^2\), you can check the units! If the units don't match, the formula is wrong.
Common Mistake to Avoid:
You can only add or subtract quantities that have the same units. You can't add 5 meters to 10 seconds. That would be like trying to add 5 apples to 10 thunderstorms—it just doesn't work!
Key Takeaway:
Units on the Left Hand Side (LHS) = Units on the Right Hand Side (RHS). If they don't match, the equation is not homogeneous.
5. Prefixes: Handling Huge and Tiny Numbers
Physics deals with things as big as the universe and as small as atoms. Instead of writing lots of zeros, we use prefixes.
The Multipliers (Memorize these!):
- T (Tera): \(10^{12}\) (Trillion)
- G (Giga): \(10^9\) (Billion)
- M (Mega): \(10^6\) (Million)
- k (kilo): \(10^3\) (Thousand)
- d (deci): \(10^{-1}\) (Tenth)
- c (centi): \(10^{-2}\) (Hundredth)
- m (milli): \(10^{-3}\) (Thousandth)
- \(\mu\) (micro): \(10^{-6}\) (Millionth)
- n (nano): \(10^{-9}\) (Billionth)
- p (pico): \(10^{-12}\) (Trillionth)
Trick for conversion: When moving from a prefix to a base unit, replace the letter with the power of 10.
Example: 5 km becomes \(5 \times 10^3\) m.
6. Labelling Graphs and Tables
In your practical work (PAGs) and exams, there is a specific way to label table headings and graph axes. We use a solidus (forward slash) to separate the quantity and the unit.
Correct Format: Quantity / unit
Examples:
- \(t\) / s (Time in seconds)
- \(v\) / m s\(^{-1}\) (Velocity in meters per second)
- \(m\) / kg (Mass in kilograms)
Why do we do this?
The slash acts like a division sign. It means the numbers in the table are "pure numbers" (the quantity divided by its unit).
7. Making Estimates
OCR wants you to be able to "eyeball" a measurement. This helps you realize if your calculated answer is ridiculous (like calculating the mass of a pencil to be 5000 kg!).
Common Estimates to Remember:
- Mass of an adult: 70 kg
- Height of a door: 2 m
- Mass of an apple: 100 g (0.1 kg)
- Speed of sound in air: 330 m s\(^{-1}\)
- Wavelength of visible light: \(400 - 700\) nm
- Atmospheric pressure: \(10^5\) Pa
Encouragement: Don't worry about being perfectly precise with estimates—being in the right "ballpark" (the right power of 10) is what matters!
Summary Checklist
Before moving to the next chapter, make sure you can:
- List the 6 S.I. base units.
- Convert derived units (like Newtons or Joules) back into base units.
- Check if an equation is homogeneous.
- Identify prefixes from pico (\(10^{-12}\)) to tera (\(10^{12}\)).
- Correctly label a graph axis using the "/" convention.
- Estimate everyday quantities like the mass of a person or the height of a room.