Physical quantities and units

Welcome to the Language of Physics!

Welcome to your first step in AS Level Physics! Before we start calculating the speed of a galaxy or the energy of an electron, we need to learn the "language" of Physics. This chapter is all about how we measure the world and how we ensure our measurements make sense. Don't worry if some of the math feels new—we will take it one step at a time!

1.1 Physical Quantities

In Physics, a physical quantity is anything that can be measured. Every physical quantity consists of two essential parts: a numerical magnitude and a unit.

Example: If you say a table is "5" long, no one knows what you mean. Is it 5 centimeters? 5 meters? 5 miles? You must say "5 meters" (5 = magnitude, meters = unit).

Making Reasonable Estimates

As a physicist, you should be able to "guess-timate" the size of things in the real world. This helps you check if your calculated answers are sensible. If you calculate the mass of a car to be 0.5 kg, you know something went wrong!

Common Estimates to Remember:
- Mass of an adult: \( 70 \text{ kg} \)
- Height of a room: \( 3 \text{ m} \)
- Mass of an apple: \( 100 \text{ g} \) (or \( 0.1 \text{ kg} \))
- Speed of sound in air: \( 330 \text{ m s}^{-1} \)
- Weight of an apple: \( 1 \text{ N} \)

Quick Review: Every measurement needs a Number + Unit. Always check if your answer "looks" right compared to real life.

1.2 SI Units (The International System)

To make sure scientists across the world understand each other, we use SI Base Units. Think of these as the "bricks" used to build every other unit in existence.

The 5 Base Units you must recall:

1. Mass: kilogram (\( \text{kg} \))
2. Length: metre (\( \text{m} \))
3. Time: second (\( \text{s} \))
4. Current: ampere (\( \text{A} \))
5. Temperature: kelvin (\( \text{K} \))

Derived Units

Most other units, like the Newton (N) or Joule (J), are called derived units because they are made by multiplying or dividing base units together.

Example: How to find the base units of Force (Newton)?
1. Start with a formula: \( F = ma \)
2. Replace with units: \( \text{Force} = \text{kg} \times \text{m s}^{-2} \)
3. So, \( 1 \text{ N} = 1 \text{ kg m s}^{-2} \)

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!

Prefixes (The Power of 10)

Physics deals with the very big and the very small. We use prefixes to keep the numbers tidy.

Small numbers:
- pico (p): \( 10^{-12} \)
- nano (n): \( 10^{-9} \)
- micro (\( \mu \)): \( 10^{-6} \)
- milli (m): \( 10^{-3} \)
- centi (c): \( 10^{-2} \)
- deci (d): \( 10^{-1} \)

Big numbers:
- kilo (k): \( 10^{3} \)
- mega (M): \( 10^{6} \)
- giga (G): \( 10^{9} \)
- tera (T): \( 10^{12} \)

Memory Aid: "King Multiplex Gets Taller" for Kilo, Mega, Giga, Tera (going up by powers of 3).

1.3 Errors and Uncertainties

No measurement is perfect. In Physics, we need to describe how imperfect they are.

Accuracy vs. Precision

These two terms are often confused in daily life, but they are different in Physics:
- Accuracy: How close your measurement is to the true value. (Hitting the bullseye).
- Precision: How close a series of measurements are to each other. (Hitting the same spot repeatedly, even if it's not the bullseye).

Random vs. Systematic Errors

1. Random Errors: These cause measurements to be scattered around the mean value. They are caused by unpredictable things like air currents or human reaction time.
Fix: Take repeat readings and calculate an average.
2. Systematic Errors: These cause readings to be constantly too high or too low. A common type is a zero error (when a scale shows 0.1g when nothing is on it).
Fix: Cannot be fixed by averaging. You must recalibrate the instrument or subtract the error.

Calculating Uncertainties

When we use measurements to calculate something new (like speed), the uncertainty carries over.

The Golden Rules:
- Adding or Subtracting: Always ADD the absolute uncertainties. \( \Delta y = \Delta a + \Delta b \)
- Multiplying or Dividing: Always ADD the percentage uncertainties. \( \% \Delta y = \% \Delta a + \% \Delta b \)
- Powers: Multiply the percentage uncertainty by the power. If \( y = x^2 \), then \( \% \Delta y = 2 \times \% \Delta x \).

Key Takeaway: Accuracy is about the "truth," precision is about "consistency." To reduce random error, repeat and average!

1.4 Scalars and Vectors

This is one of the most important concepts in AS Physics. Every quantity is either a scalar or a vector.

Definitions

- Scalar: Has magnitude (size) only.
Examples: Distance, Speed, Mass, Time, Energy.
- Vector: Has magnitude AND direction.
Examples: Displacement, Velocity, Acceleration, Force, Momentum.

Adding Vectors

You cannot simply add vector numbers unless they are in the same direction. We use the "Tip-to-Tail" method:
1. Draw the first vector.
2. Draw the second vector starting from the "tip" (arrowhead) of the first one.
3. The resultant is the line drawn from the very start to the very end.

Resolving Vectors (The Component Method)

Sometimes it is easier to break a diagonal vector into two perpendicular parts (horizontal and vertical). Imagine a force \( F \) at an angle \( \theta \) to the horizontal:

- Horizontal Component: \( F_x = F \cos \theta \)
- Vertical Component: \( F_y = F \sin \theta \)

Simple Trick: The side "CO-signed" to the angle is COS. (The component touching the angle \( \theta \) uses \( \cos \theta \)).

Common Mistake to Avoid: Don't forget that direction matters! In vectors, going "Left" or "Down" is often treated as negative, while "Right" or "Up" is positive.

Summary: You've now learned how to define quantities, use the correct SI units, handle measurement errors, and work with vectors. These are the building blocks you will use in every single chapter that follows. Great job!