Welcome to the World of Measurement!
In Physics, we don't just say things are "big" or "fast." We need to measure them exactly. Imagine trying to build a bridge where one engineer uses "paces" and another uses "feet"—it would be a disaster! To avoid this, scientists use a standardized system called the S.I. units (Système International). In this chapter, you’ll learn the language of Physics: how we label the universe and how to make sure our equations actually make sense.
Quick Review: Every physical quantity consists of two parts: a numerical value and a unit. For example, in 5.0 kg, "5.0" is the value and "kg" is the unit. Without the unit, the number is meaningless!
1. The 6 S.I. Base Units
Think of base units as the "LEGO bricks" of Physics. Every other unit in the universe is built by combining these six basic ones. While there are seven in total, your OCR syllabus focuses on these specific six:
- Length: metre (\(m\))
- Mass: kilogram (\(kg\))
- Time: second (\(s\))
- Electric Current: ampere (\(A\))
- Temperature: kelvin (\(K\))
- Amount of substance: mole (\(mol\))
Memory Aid: Use the mnemonic "My Large Tiger Always Takes Milk" (Mass, Length, Time, Ampere, Temperature, Mol) to remember them!
Did you know? The kilogram is the only base unit that already has a prefix ("kilo") in its name. Even though a gram exists, the kilogram is the official base unit.
Key Takeaway: All measurements in Physics should eventually be traceable back to these six base units.
2. Derived Units
When we combine base units using multiplication or division, we get derived units. For example, to find speed, we divide distance (metres) by time (seconds), giving us the unit \(m \ s^{-1}\).
How to find the base units of a derived quantity:
If you encounter a unit like the Newton (N) or Joule (J), you can break it down step-by-step using a formula you know.
Step-by-Step Example: Finding the base units of Force (\(F\))
1. Pick a simple formula for the quantity: \(F = ma\) (Force = mass \(\times\) acceleration).
2. Replace the quantities with their units: Mass is \(kg\). Acceleration is \(m \ s^{-2}\).
3. Combine them: The base units of a Newton are \(kg \ m \ s^{-2}\).
Common Examples:
Density: \(\rho = \frac{m}{V}\) \(\rightarrow\) \(kg \ m^{-3}\)
Momentum: \(p = mv\) \(\rightarrow\) \(kg \ m \ s^{-1}\)
Key Takeaway: If you forget a derived unit, don't panic! Just use a simple formula to work it out from the base units.
3. Checking Homogeneity (Does the math work?)
In Physics, an equation must be homogeneous. This is a fancy way of saying that the units on the left side must be exactly the same as the units on the right side.
Analogy: You can't add 3 apples to 2 oranges and get 5 bananas. Similarly, you can't add a "length" to a "time."
Example: Checking \(s = ut + \frac{1}{2}at^2\)
- Left side (\(s\)): unit is \(m\).
- Right side term 1 (\(ut\)): \((m \ s^{-1}) \times (s) = m \ s^{0} =\) \(m\).
- Right side term 2 (\(\frac{1}{2}at^2\)): \((m \ s^{-2}) \times (s^2) = m \ s^{0} =\) \(m\). (Note: numbers like \(\frac{1}{2}\) have no units!)
Since every term is in metres, the equation is homogeneous.
Common Mistake: Forgetting that every single term separated by a plus or minus sign must have the same units. If you are adding two things together, they must have the same units!
Key Takeaway: Checking homogeneity is a great way to check if you've remembered a formula correctly during an exam.
4. Unit Prefixes
Physics deals with the very large (galaxies) and the very small (atoms). We use prefixes to avoid writing too many zeros. You need to memorize these for your exam:
The Big Ones (Multiples):
- tera (T): \(10^{12}\)
- giga (G): \(10^{9}\)
- mega (M): \(10^{6}\)
- kilo (k): \(10^{3}\)
The Small Ones (Submultiples):
- deci (d): \(10^{-1}\)
- centi (c): \(10^{-2}\)
- milli (m): \(10^{-3}\)
- micro (\(\mu\)): \(10^{-6}\)
- nano (n): \(10^{-9}\)
- pico (p): \(10^{-12}\)
Don't worry if this seems tricky! Most students find it helpful to practice converting back to the "standard" form. For example, if you see \(5 \ pF\) (picofarads), immediately write it as \(5 \times 10^{-12} \ F\).
Quick Review Box:
Standardizing units: Always convert to S.I. base units (or their standard derived form) before plugging numbers into a calculation!
5. Conventions for Graphs and Tables
When you draw a table or a graph in Physics, there is a specific rule you must follow: use a solidus (/) to separate the quantity from the unit.
The Rule: Quantity / unit
Examples:
- Speed / \(m \ s^{-1}\)
- Time / \(s\)
- Temperature / \(K\)
Why do we do this? It makes the data in the table "pure numbers." If the column heading is Length / m and the value is 0.5, it literally means: "The length divided by 1 metre equals 0.5." It keeps everything neat and mathematically sound!
Key Takeaway: Always label your axes and table headers as Variable / unit. Avoid using brackets like Speed (m/s), as the solidus is the preferred A-Level convention.
6. Making Estimates
The syllabus requires you to be able to make estimates of physical quantities. This is often called "order of magnitude" thinking.
Try these "common sense" anchors:
- Mass of an adult: \(\approx 70 \ kg\)
- Height of a door: \(\approx 2 \ m\)
- Mass of an apple: \(\approx 100 \ g\) (\(0.1 \ kg\))
- Atmospheric pressure: \(\approx 10^{5} \ Pa\)
- Speed of sound in air: \(\approx 300 \ m \ s^{-1}\)
Key Takeaway: If a calculation gives you the mass of a car as \(0.005 \ kg\), use your estimating skills to realize something has gone wrong!