CIE iGCSE Co-ordinated Sciences-P1.1 Physical quantities and measurement techniques- Study Notes- New Syllabus
CIE iGCSE Co-ordinated Sciences-P1.1 Physical quantities and measurement techniques – Study Notes
CIE iGCSE Co-ordinated Sciences-P1.1 Physical quantities and measurement techniques – Study Notes -CIE iGCSE Co-ordinated Sciences – per latest Syllabus.
Key Concepts:
Core
- Describe the use of rulers and measuring cylinders to find a length or a volume.
- Describe how to measure a variety of time intervals using clocks and digital timers.
- Determine an average value for a small distance and for a short interval of time by measuring multiples (including the period of oscillation of a pendulum).
Supplement
- Understand that a scalar quantity has magnitude (size) only and that a vector quantity has magnitude and direction.
- Know that the following quantities are scalars: distance, speed, time, mass, energy and temperature.
- Know that the following quantities are vectors: force, weight, velocity, acceleration and gravitational field strength.
CIE iGCSE Co-Ordinated Sciences-Concise Summary Notes- All Topics
Measuring Length and Volume
Measuring Length with a Ruler 
A ruler or metre rule is a simple instrument used to measure short lengths.
- It is usually marked in millimetres (mm) and centimetres (cm).
To measure correctly:
- Place the object along the ruler with one end at the zero mark (not at the edge).
- Look at the reading directly from above to avoid parallax error.
- For more accuracy, use the scale with the smallest divisions.
Example: A notebook placed along a ruler starts at 0.0 cm and ends at 18.7 cm. Length of notebook = \( 18.7~\text{cm} \).
Measuring Volume with a Measuring Cylinder
A measuring cylinder is used for finding the volume of liquids and irregular solids.
- It has a scale marked in millilitres (mL) or cubic centimetres (cm³).
Correct method:
- Place the cylinder upright on a flat surface.
- Read the volume at the bottom of the meniscus (the curved water surface).
For an irregular solid, use the displacement method:
- Record initial water volume (\( V_1 \)).
- Submerge the object fully and record final volume (\( V_2 \)).
- Volume of object = \( V_2 – V_1 \).
Example: A marble raises the water level in a cylinder from 50 mL to 62 mL. Volume of marble = \( 62 – 50 = 12~\text{mL} \).
Example:
You measure a pen using a ruler. One end is at 1.2 cm and the other at 15.6 cm. Find the length.
▶️ Answer/Explanation
Initial position = \( 1.2~\text{cm} \)
Final position = \( 15.6~\text{cm} \)
Length = \( 15.6 – 1.2 = \boxed{14.4~\text{cm}} \)
Example :
A stone is dropped in water inside a measuring cylinder. Water rises from 72 mL to 91 mL. What is the stone’s volume?
▶️ Answer/Explanation
Initial volume = \( 72~\text{mL} \)
Final volume = \( 91~\text{mL} \)
Stone volume = \( 91 – 72 = \boxed{19~\text{mL}} \)
Measuring Time Intervals
Time is a fundamental physical quantity. Its SI unit is the second (s).
- Time intervals can be measured using clocks or digital timers, depending on the situation.
Measuring Time with a Clock
Stop-clocks (analogue) are designed for measuring short to medium intervals.
- They usually have a start/stop button and a reset button.
- Common uses:
- Timing the duration of an experiment in the lab.
- Measuring a student’s reaction time in a test.
- Accuracy: limited to the smallest division on the dial (usually 0.1 s or 1 s).
Example: A chemical reaction starts when a solution is mixed and ends when the colour changes. Start the clock at mixing, stop when colour changes → measured time = \( 52~\text{s} \).
Measuring Time with a Digital Timer
Digital timers display time electronically, often with millisecond precision.
- They are more accurate and easier to read than analogue stop-clocks.
- Common uses:
- Timing oscillations of a pendulum.
- Measuring sprint races in sports.
- Recording very short intervals in physics experiments (e.g. free fall).
- Digital timers often have a lap function to record multiple intervals in succession.
Example: A pendulum swings 10 complete oscillations in 15.4 s (measured with a digital timer). Time for one oscillation = \( \tfrac{15.4}{10} = 1.54~\text{s} \).
Example:
You use a stop-clock to measure how long it takes a toy car to roll down a ramp. The timer shows 4.8 seconds. What is the time interval?
▶️ Answer/Explanation
Start the timer when the car is released.
Stop the timer when the car reaches the end of the ramp.
Time interval = \(\boxed{4.8~\text{s}}\)
Example:
A student measures the time for 20 swings of a pendulum using a digital timer. Total time recorded = 31.2 s. Find the time period of one swing.
▶️ Answer/Explanation
Total time = \( 31.2~\text{s} \)
Number of oscillations = \( 20 \)
Time for one oscillation = \( \tfrac{31.2}{20} = \boxed{1.56~\text{s}} \)
Determining an Average Value from Multiples
When a distance or time interval is very small, a single measurement may be inaccurate due to reaction time or reading error.To reduce error, measure many multiples of the same quantity and then calculate the average.
Small Distance
If a distance is too small to measure directly, measure the length of several identical intervals and divide.
Method:
- Arrange several identical objects in a line (e.g. 20 paper clips).
- Measure the total length with a ruler.
- Average length of one object $\mathrm{= (Total length) ÷ (Number of objects).}$
Example: 25 identical paper clips placed in a row have a total length of 37.5 cm. Length of one paper clip = \( \tfrac{37.5}{25} = 1.50~\text{cm} \).
Short Time Interval
Measuring one very short interval with a stopwatch is inaccurate (due to human reaction time).Instead, measure many intervals and calculate the average.
Method (Pendulum):
- Start the timer when the pendulum passes the central point.
- Count a number of complete oscillations (e.g. 20 swings).
- Record the total time.
- Period of one oscillation $\mathrm{= (Total time) ÷ (Number of oscillations).}$
Example: Time for 30 oscillations = 45.9 s. Average period = \( \tfrac{45.9}{30} = 1.53~\text{s} \).
Example:
10 identical metal balls are placed in a row. The total measured length is 12.4 cm. Find the average diameter of one ball.
▶️ Answer/Explanation
Total length = \( 12.4~\text{cm} \)
Number of balls = 10
Average diameter = \( \tfrac{12.4}{10} = \boxed{1.24~\text{cm}} \)
Example :
A student measures the time for 40 swings of a pendulum as 61.2 s. What is the time period of one swing?
▶️ Answer/Explanation
Total time = \( 61.2~\text{s} \)
Number of oscillations = 40
Time period = \( \tfrac{61.2}{40} = \boxed{1.53~\text{s}} \)
Scalar Quantities
A scalar quantity has only magnitude (size) but no direction.
- Scalars are completely described by a number and a unit.
- Example: “A mass of 5 kg” tells us everything — no direction is needed.
Examples of Scalar Quantities
- Distance – how much ground an object covers (m).
- Speed – how fast something moves (m/s).
- Time – duration of an event (s).
- Mass – amount of matter in an object (kg).
- Energy – ability to do work (J).
- Temperature – measure of hotness or coldness (°C or K).
Note: Scalars do not involve direction, so they can be added or compared like ordinary numbers.
Example:
A runner covers 400 m, then another 200 m. What is the total distance travelled?
▶️ Answer/Explanation
Distance is a scalar → only magnitude matters.
Total distance = \( 400 + 200 = \boxed{600~\text{m}} \)
Example:
A car moves at a speed of 20 m/s for 15 s. What distance does it travel?
▶️ Answer/Explanation
Distance = Speed × Time
= \( 20 \times 15 = \boxed{300~\text{m}} \)
Vector Quantities
To describe a vector fully, you must state how large it is and which direction it acts in.
- Vectors are often represented by arrows:
- Length of the arrow → magnitude
- Arrowhead → direction
Examples of Vector Quantities
- Force – a push or pull (N).
- Weight – force due to gravity (N, always acts downward).
- Velocity – speed in a specific direction (m/s).
- Acceleration – rate of change of velocity (m/s²).
- Gravitational field strength – force per unit mass, direction is towards the attracting body (N/kg).
Note: When adding vectors, both magnitude and direction must be considered (e.g. using scale diagrams or vector components).
Example:
A person walks 3 km east and then 4 km north. Find their resultant displacement.
▶️ Answer/Explanation
Displacement is a vector → use Pythagoras’ theorem.
Resultant displacement = \( \sqrt{3^2 + 4^2} = 5~\text{km} \).
Direction = \( \tan^{-1}(4/3) = 53^\circ \) north of east.
Final answer: \( \boxed{5~\text{km at } 53^\circ \text{ N of E}} \)
Example :
A car has a velocity of 12 m/s east. After speeding up, its velocity becomes 20 m/s east. What is the acceleration if this change happens in 4 s?
▶️ Answer/Explanation
$\rm{Acceleration = Change in velocity ÷ Time}$
= \( (20 – 12) / 4 = 2~\text{m/s}^2 \) east.
Since acceleration is a vector, the direction is east.
Final answer: \( \boxed{2~\text{m/s}^2 \text{ east}} \)