Welcome to the Foundations of Physics!
Hi there! Welcome to the very first step of your A Level Physics journey. Before we can dive into the secrets of the universe, we need to learn the language of Physics. Just like you can't write a great story without knowing grammar, you can't do Physics without understanding physical quantities and units. In this chapter, we will learn how to measure the world around us and how to make sure our equations actually make sense. Don't worry if it seems like a lot of definitions at first—once you see how they fit together, it becomes much easier!
1. What is a Physical Quantity?
In Physics, a physical quantity is anything that can be measured. Every physical quantity consists of two vital parts: a numerical value and a unit.
Think of it like this: If you tell a friend you are "6" tall, they won't know if you mean 6 feet (tall), 6 inches (tiny), or 6 meters (a giant!). The unit gives the number meaning.
The Rule: Physical Quantity = Value \(\times\) Unit
Example: The length of a table is 1.5 m. "1.5" is the value, and "m" (meters) is the unit.
Quick Review: The "Why"
Did you know? In 1999, NASA lost a \$125 million Mars orbiter because one engineering team used imperial units (inches) while another used metric units (meters). Units aren't just for exams—they save spacecraft!
2. The S.I. System (The Golden Six)
To keep everyone on the same page, scientists use the Système Internationale (S.I.). There are six base quantities you need to know for the OCR syllabus. Everything else in Physics is built from these six.
1. Mass: measured in kilograms (kg)
2. Length: measured in meters (m)
3. Time: measured in seconds (s)
4. Electric Current: measured in amperes (A)
5. Temperature: measured in kelvin (K)
6. Amount of Substance: measured in moles (mol)
Memory Aid (Mnemonic):
Many Lions Take Care To Act (Mass, Length, Time, Current, Temperature, Amount).
Common Mistake: Many students think the base unit for mass is the gram. It is actually the kilogram (kg)! Also, remember that for temperature, we use Kelvin, not Celsius.
Key Takeaway: Every measurement in Physics can be traced back to these six base units.
3. Derived Units
If the base units are the "bricks," derived units are the buildings we create with them. We get derived units by multiplying or dividing base units together.
Example 1: Speed
Speed = distance / time.
Units = \(m / s\) or \(\text{m s}^{-1}\).
Example 2: Density (\(\rho\))
Density = mass / volume.
Units = \(kg / m^3\) or \(\text{kg m}^{-3}\).
Example 3: Force (The Newton)
Force = mass \(\times\) acceleration.
Acceleration is \(\text{m s}^{-2}\).
So, 1 Newton (N) is actually \(\text{kg m s}^{-2}\) in base units.
Key Takeaway: When asked to show a unit in "S.I. Base Units," you must break it down until you only see kg, m, s, A, K, or mol.
4. Unit Prefixes
Physics deals with the very big (stars) and the very small (atoms). We use prefixes to avoid writing too many zeros.
The Big Ones (Multiples):
- kilo (k): \(10^3\) (thousand)
- mega (M): \(10^6\) (million)
- giga (G): \(10^9\) (billion)
- tera (T): \(10^{12}\) (trillion)
The Small Ones (Sub-multiples):
- deci (d): \(10^{-1}\)
- centi (c): \(10^{-2}\)
- milli (m): \(10^{-3}\)
- micro (\(\mu\)): \(10^{-6}\)
- nano (n): \(10^{-9}\)
- pico (p): \(10^{-12}\)
Step-by-Step Conversion: To convert 5 Megawatts (MW) to Watts (W), replace the 'M' with its value: \(5 \times 10^6 \text{ W}\). To go the other way, divide by the prefix value.
Key Takeaway: Learn the power of ten associated with each symbol. A capital 'M' (Mega) is very different from a lowercase 'm' (milli)!
5. Checking Homogeneity
An equation is homogeneous if the units on the left-hand side (LHS) are exactly the same as the units on the right-hand side (RHS). This is like a "spell-check" for Physics.
How to check homogeneity:
1. Write out the equation.
2. Replace every quantity with its S.I. base units.
3. Simplify both sides.
4. If they match, the equation is homogeneous (it could be correct). If they don't match, the equation is definitely wrong!
Example: Check \(s = ut + \frac{1}{2}at^2\)
LHS: \(s\) is distance = m
RHS: \(ut\) is \((\text{m s}^{-1} \times \text{s}) = \text{m}\).
RHS: \(at^2\) is \((\text{m s}^{-2} \times \text{s}^2) = \text{m}\). (Note: numbers like \(\frac{1}{2}\) have no units).
Since both terms on the right are "m" and the left is "m", the equation is homogeneous.
Key Takeaway: You can only add or subtract quantities that have the same units. You can't add 5 meters to 10 seconds!
6. Making Estimates
As a physicist, you need to have a "feel" for numbers. The exam might ask you to estimate a value. You don't need to be exact, just "in the right ballpark" (the correct power of ten).
Common Estimates to Remember:
- Mass of an adult: ~70 kg
- Height of a room: ~2.5 m
- Mass of a car: ~1000 kg
- Walking speed: ~1 \(\text{m s}^{-1}\)
- Atmospheric pressure: ~\(10^5 \text{ Pa}\)
- Energy of a snack bar: ~\(10^6 \text{ J}\) (1 Megajoule)
Encouragement: Don't panic if you don't know the exact weight of a blue whale! Just compare it to things you do know. Is it heavier than a car? Yes. Is it heavier than a house? Probably. A sensible guess like \(10^5 \text{ kg}\) is better than no guess at all.
7. Conventions for Tables and Graphs
When you record data, there is a specific way to label your headers. We use a forward slash to separate the quantity and the unit.
The Format: Quantity / Unit
Examples:
- \(L / \text{m}\) (Length in meters)
- \(t / \text{s}\) (Time in seconds)
- \(v / \text{m s}^{-1}\) (Speed in meters per second)
Why? This mathematically means "Value = Physical Quantity divided by Unit." It leaves just the pure number in the table or on the graph axis.
Key Takeaway: Never put units in the individual cells of a table. Put them once at the top in the header using the forward slash convention!
Chapter Summary
1. Physical Quantities: Must have a value and a unit.
2. Base Units: The 6 essentials (kg, m, s, A, K, mol).
3. Derived Units: Combinations of base units (like \(\text{kg m s}^{-2}\) for Force).
4. Prefixes: Handy shortcuts for powers of ten (like kilo-, mega-, micro-).
5. Homogeneity: Both sides of an equation must have matching base units.
6. Labelling: Always use the "Quantity / Unit" format for tables and graphs.