Physical Quantities and Measurement Techniques (Syllabus 1.1)
Hello future Physicists! This chapter is your foundation. Before we can talk about big ideas like motion and energy, we need to know how to measure things accurately. This is where we learn the essential tools and techniques used in every single experiment you will ever do in Physics.
Don't worry if this seems tricky at first; we'll break down the practical skills step-by-step!
1. Measuring Length and Volume (Core Content)
1.1 Measuring Length (Rulers)
The most basic tool for measuring distance (or length) is the ruler or measuring tape. In IGCSE Physics, we usually measure in metres (m), centimetres (cm), or millimetres (mm).
- Always ensure the ruler is aligned correctly, starting exactly at the zero mark.
- Read the measurement directly opposite the object's edge.
- Avoid parallax error: this is the error caused by reading the scale from an angle. Always look straight down at the scale.
Quick Tip: If the zero end of your ruler is damaged, don't use it! Start your measurement from the 1 cm mark and subtract 1 cm from the final reading.
1.2 Measuring the Volume of Liquids (Measuring Cylinders)
Liquids are usually measured using a measuring cylinder (or graduated cylinder). Volume is measured in cubic metres (\(m^3\)), cubic centimetres (\(cm^3\)), or litres (L).
- Pour the liquid into the cylinder.
- The surface of the liquid will often curve slightly, forming a shape called a meniscus.
- When reading the volume, always read the bottom of the meniscus.
- You must read the scale at eye level to avoid parallax error.
1.3 Measuring the Volume of Irregular Solids (Displacement Method)
If you have an object like a stone, you can't use a ruler to find its dimensions. Instead, you use the concept of volume by displacement.
This method works because the volume of water pushed out (displaced) is equal to the volume of the object.
Step-by-Step Displacement:
- Partially fill a measuring cylinder with water and record the initial volume, \(V_1\).
- Gently lower the irregular solid (like a key or small stone) into the water using a thread so that it is fully submerged.
- Record the final volume, \(V_2\).
- The volume of the object, \(V\), is calculated by finding the difference: $$V = V_2 - V_1$$
2. Measuring Time Intervals (Core Content)
2.1 Using Clocks and Digital Timers
Time intervals are measured using clocks and digital timers, typically in seconds (s).
- Digital timers are generally preferred in science experiments as they are more accurate, often measuring up to 0.01 s.
- When using a stopwatch, the main source of error is often human reaction time (starting and stopping the timer too late or too early).
2.2 Improving Accuracy: Measuring Multiples (Core 3)
To reduce the error caused by reaction time, especially when measuring very short time intervals or small distances, we measure a multiple of the quantity and then calculate the average.
A. Averaging Small Distances
Imagine you need to find the thickness of a single sheet of paper (which is very thin).
Method:
- Measure the total thickness of a stack of 100 sheets using a ruler.
- Divide the total thickness by 100.
Example: If 100 sheets measure 1.0 cm, then one sheet's thickness is \(1.0 \, \text{cm} / 100 = 0.01 \, \text{cm}\). This is much more accurate than trying to measure one sheet directly!
B. Averaging Short Time Intervals (Pendulum Period)
The period (T) of a pendulum is the time taken for one complete swing (one oscillation).
Since the period is often less than a few seconds, timing one swing is highly inaccurate due to reaction time.
Method:
- Start the pendulum swinging.
- Time the duration for 20 complete oscillations (e.g., \(t_{20}\)).
- Calculate the average period (T) by dividing the total time by the number of swings: $$\text{Average Period (T)} = \frac{\text{Total Time for 20 swings}}{20}$$
Why 20? By timing 20 swings, your reaction time error (which happens twice—start and stop) is spread out over a longer time, making the calculated period much more precise.
3. Scalars and Vectors (Supplement Content)
As you progress in Physics, you will deal with many different types of quantities. We need to distinguish between those that only have size and those that also have direction.
3.1 Defining Scalars
A scalar quantity is defined as a physical quantity that has magnitude (size) only.
- It does not have a direction associated with it.
- Analogy: If you say you ran 5 km, the '5 km' is the scalar quantity. The direction you ran doesn't matter for the distance.
3.2 Examples of Scalar Quantities (Supplement 5)
You must know the key scalar quantities for the exam:
- Distance
- Speed
- Time
- Mass
- Energy
- Temperature
3.3 Defining Vectors
A vector quantity is defined as a physical quantity that has magnitude (size) AND direction.
- Direction is essential for a vector quantity.
- Analogy: If you say a plane flew 500 km/h North, the 'North' is the required direction, making the measurement a vector.
3.4 Examples of Vector Quantities (Supplement 6)
You must know the key vector quantities for the exam:
- Force
- Weight (Force due to gravity)
- Velocity (Speed in a given direction)
- Acceleration
- Momentum
- Electric field strength
- Gravitational field strength
Memory Aid: Think of the letter 'V'. If a quantity starts with V (Velocity) or contains an element of direction/Variation (Vector), it’s usually a vector! Also remember that Forces are always vectors.
Students often confuse mass and weight. Mass is a scalar (it’s just the amount of matter), but Weight is a vector because it is the force of gravity acting downwards.
4. Resultant Vectors (Supplement Content)
When multiple forces or velocities act on an object, the overall effect is described by the resultant vector. This is a single vector that has the same effect as all the original vectors combined.
4.1 Resultant of Two Vectors at Right Angles (90°) (Supplement 7)
In the IGCSE syllabus, you only need to deal with finding the resultant of two vectors that act at a right angle (perpendicular to each other), usually forces or velocities.
A. Calculation Method (Using Pythagoras)
If two vectors, A and B, act at 90° to each other, the resultant vector (R) forms the hypotenuse of a right-angled triangle.
We use the Pythagorean theorem to find the magnitude (size) of R:
$$R^2 = A^2 + B^2$$Therefore, the magnitude of the resultant is: $$R = \sqrt{A^2 + B^2}$$
Example: A boat is moving due North at 3 m/s (Vector A) while a strong current pushes it due East at 4 m/s (Vector B). What is the resultant velocity (R)?
$$R = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25}$$ $$R = 5 \, \text{m/s}$$
B. Graphical Method (Scale Drawing)
For more complex problems, or when asked to find the resultant graphically, you must use a scale diagram:
- Choose an appropriate scale (e.g., 1 cm = 1 N, or 1 cm = 1 m/s).
- Draw the first vector (A) to scale.
- From the tip (head) of Vector A, draw the second vector (B) to scale, ensuring it is drawn exactly perpendicular (90°) to A.
- Draw the resultant vector (R) from the start (tail) of A to the tip (head) of B.
- Measure the length of R with a ruler and use your scale to determine the magnitude of the resultant.
- Measure the angle (usually to the horizontal or vertical) using a protractor to find the direction of the resultant.
Think of it like directions on a treasure map: you start at X, go 3 km North, then 4 km East. The straight line from X to your end point is the resultant vector.