Learning Outcomes
What You Will Learn
Student Learning Outcomes (SLOs) as defined by FBISE for Unit 1.
Differentiate between physical and non-physical quantities
Distinguish between base and derived quantities and their SI units
Apply the seven SI base units and derive other units from them
Analyse and express numerical data using scientific notation and prefixes
Differentiate between scalar and vector quantities with examples
Determine the resultant of two vectors at right angles
Justify and illustrate the use of metre rule, vernier caliper, and screw gauge
Differentiate between systematic and random errors, and how to reduce them
Differentiate between precision and accuracy in measurements
Determine and apply rules for significant figures and rounding off
Physics Unit 1 — Complete Notes
Full chapter with all diagrams, instrument readings, worked examples & exercise solutions
SI System
Seven SI Base Units
All physical quantities in science are measured using these seven fundamental units.
m
Meter
Length
kg
Kilogram
Mass
s
Second
Time
A
Ampere
Electric Current
K
Kelvin
Temperature
mol
Mole
Amount of Substance
cd
Candela
Light Intensity
Derived Units
Common Derived Units
Obtained by multiplying or dividing base units.
| Quantity | Symbol | SI Unit Name | In Base Units |
|---|---|---|---|
| Area | A | Square meter | m² |
| Volume | V | Cubic meter | m³ |
| Speed / Velocity | v | Meter per second | ms⁻¹ |
| Acceleration | a | Meter per second² | ms⁻² |
| Density | ρ | kg per cubic meter | kgm⁻³ |
| Force | F | Newton (N) | kgms⁻² |
| Pressure | P | Pascal (Pa) | kgm⁻¹s⁻² |
| Energy | E, U | Joule (J) | kgm²s⁻² |
Powers of Ten
SI Prefixes
Prefixes make it easier to write very large or very small quantities without scientific notation.
10¹⁸
Exa
Symbol: E
10¹⁵
Peta
Symbol: P
10¹²
Tera
Symbol: T
10⁹
Giga
Symbol: G
10⁶
Mega
Symbol: M
10³
Kilo
Symbol: k
10²
Hecto
Symbol: h
10¹
Deca
Symbol: da
10⁻¹
Deci
Symbol: d
10⁻²
Centi
Symbol: c
10⁻³
Milli
Symbol: m
10⁻⁶
Micro
Symbol: μ
10⁻⁹
Nano
Symbol: n
10⁻¹²
Pico
Symbol: p
10⁻¹⁵
Femto
Symbol: f
10⁻¹⁸
Atto
Symbol: a
Lab Instruments
Measuring Instruments
Each instrument has a different least count — the smaller the least count, the more precise the measurement.
Metre Rule
L.C. = 1 mm
A 1-metre long physics lab tool with 1000 millimetre divisions. Used for measuring lengths of everyday objects. The rulers on your stationery are shorter versions of a metre rule.
Vernier Caliper
L.C. = 0.1 mm
Measures thickness, diameter, and width of objects and internal/external diameter of hollow cylinders. Uses a sliding vernier scale to measure fractions of a millimetre. Digital version: L.C. = 0.01 mm.
Screw Gauge
L.C. = 0.01 mm
The most precise length-measuring instrument in the lab. Measures by rotating a circular (thimble) scale over a linear scale. Pitch = 0.5 mm, Circular divisions = 50. Used to measure wire diameters and thin sheets.
Physical Balance
Milligram order
The first mass-measuring instrument ever invented. A very sensitive beam balance with two pans, placed in a protective glass case. Standard weights from a weight box are used to find the mass of a body.
Measuring Cylinder
L.C. = 1 cm³
Also called a graduated cylinder. Used to measure the volume of liquids in mL or cm³. Can also be used to find the volume of irregular solids by water displacement: Volume = V₂ − V₁.
Stop Watch
Digital L.C. = 0.1 s
Measures specific time intervals. Mechanical (analogue) type: L.C. = 1 s. Digital type: L.C. = 0.1 s. Used to measure the period of a pendulum, reaction times, and other time intervals in experiments.
PART 1
Physics, Quantities & SI Units
Introduction to Physics
1. What is physics? What do we study in it?
• Define physics.• What is the most fundamental science?
Physics is the most fundamental of all natural sciences. In physics, we study matter, energy, and their interaction. The laws and principles of physics help us to understand nature.
📝 In the 19th century, physical sciences were divided into five disciplines: physics, chemistry, astronomy, geology, and meteorology.
2. How is physics related to technology? Give examples.
• What is the role of physics in modern technology?• Name some technologies based on physics.
All technologies are based on the principles of physics — from everyday devices like computers, smartphones, and the internet, to advanced ones like rockets, magnetically levitating trains, and microscopic robots that fight cancer cells. Physics is behind every technology and plays a key role in further development of technologies such as airplanes, PET scans, and nuclear systems.
3. Name the major branches of physics.
• List the main divisions of physics.• Are the branches of physics fixed in number?
The major branches include Mechanics, Optics, Thermodynamics, Oscillations and Waves, Electromagnetism, Astrophysics, Quantum Physics, Atomic and Nuclear Physics, and Relativity. The branches are continuously increasing as technology progresses.
📝 The cubit — the unit used by Egyptians to build the pyramids — is the distance from the elbow to the tip of the middle finger when the arm is extended.
Physical Quantities & Units
1. What are physical quantities? How do they differ from non-physical quantities?
• Define physical quantities and give examples.• What are non-physical quantities?
Physical quantities are those which can be measured — e.g., length, mass, time, density, temperature. Non-physical quantities cannot be measured — e.g., taste, feeling, and color.
📝 Measurement = a comparison between an unknown physical quantity and a standard. A unit is the standard with which physical quantities are compared.
2. Distinguish between base and derived physical quantities.
• Define base quantities and derived quantities.• How are derived quantities obtained?
Base (fundamental) quantities — like mass, length, and time — are the simplest form of physical quantities from which all others can be derived.
Derived quantities are obtained by multiplying or dividing base quantities. Examples: Speed = length ÷ time (m/s), Area = length × length (m²), Density = mass ÷ volume (kg/m³).
Derived quantities are obtained by multiplying or dividing base quantities. Examples: Speed = length ÷ time (m/s), Area = length × length (m²), Density = mass ÷ volume (kg/m³).
3. What is the SI system? How many base units does it have?
• Define System International (SI).• What does SI stand for?
SI stands for Système International d'Units (French for "International System of Units"). It is the internationally accepted system of units. In SI, seven (7) physical quantities are chosen as base and their units defined and standardized. All other units are derived from these seven.
number = numerical magnitude × unit | e.g., 1.65 metres
PART 2
Scientific Notation & Scalars vs Vectors
Scientific Notation & Prefixes
1. What is scientific notation? Why do we use it?
• Define standard form or scientific notation.• What is a mantissa and exponent?
Scientific notation is an easy method of writing very large or very small numbers in powers of ten:
number = mantissa × 10exponent
where the mantissa is greater than 1 and less than 10. We use it because very large/small numbers are time-consuming to write and prone to error. Example: Mass of Earth = 5.98 × 10²⁴ kg; Diameter of proton = 1.7 × 10⁻¹⁵ m.2. What are prefixes? Give examples of common prefixes.
• Define prefix in physics.• What is the prefix for 10⁶, 10⁻³, 10⁻⁹?
A prefix is a name given to a specific power of ten, making it easier to express large or small quantities. Common ones:
• Mega (M) = 10⁶ • Kilo (k) = 10³ • Milli (m) = 10⁻³
• Micro (μ) = 10⁻⁶ • Nano (n) = 10⁻⁹ • Pico (p) = 10⁻¹²
• Femto (f) = 10⁻¹⁵ • Giga (G) = 10⁹ • Tera (T) = 10¹²
• Mega (M) = 10⁶ • Kilo (k) = 10³ • Milli (m) = 10⁻³
• Micro (μ) = 10⁻⁶ • Nano (n) = 10⁻⁹ • Pico (p) = 10⁻¹²
• Femto (f) = 10⁻¹⁵ • Giga (G) = 10⁹ • Tera (T) = 10¹²
📝 Example: 1 ton = 1.0 × 10⁶ g = 1.0 Mg (Megagram)
Scalars and Vectors
1. Differentiate between scalar and vector quantities with examples.
• What are scalar quantities? Give examples.• What are vector quantities? Give examples.
Scalar quantities are completely described by magnitude alone (no direction needed): distance, speed, time, mass, energy, temperature.
Vector quantities require both magnitude AND direction: displacement, force, weight, velocity, acceleration, momentum, electric field strength, gravitational field strength.
Vector quantities require both magnitude AND direction: displacement, force, weight, velocity, acceleration, momentum, electric field strength, gravitational field strength.
⚠️ Scalars use ordinary algebra; vectors use vector algebra — they cannot be added by simply adding their values.
2. How is a vector represented and added graphically?
• How is a vector shown symbolically and graphically?• What is the head-to-tail method? What is a resultant vector?
Symbolic: A letter with an arrow overhead — e.g., F⃗ or bold F.
Graphical: An arrow whose length represents magnitude (to scale) and whose arrowhead shows direction.
Head-to-tail method: Place vectors head to tail drawn to scale. Join the tail of the first to the head of the last — this gives the resultant vector R.
For two perpendicular vectors A and B: R = √(A² + B²)
Graphical: An arrow whose length represents magnitude (to scale) and whose arrowhead shows direction.
Head-to-tail method: Place vectors head to tail drawn to scale. Join the tail of the first to the head of the last — this gives the resultant vector R.
For two perpendicular vectors A and B: R = √(A² + B²)
PART 3
Measuring Instruments in Detail
Vernier Caliper
1. What is a vernier caliper? What can it measure?
• Define vernier caliper.• What are the two scales on a vernier caliper?
A vernier caliper is a device used to measure a fraction of a smallest division on scale by sliding another scale over it. It can measure the thickness, diameter, or width of objects, and the internal/external diameter of hollow cylinders.
It has two scales: a main scale (1 mm divisions) and a sliding vernier scale. Its least count is:
It has two scales: a main scale (1 mm divisions) and a sliding vernier scale. Its least count is:
Least Count = Smallest division on main scale ÷ Total divisions on vernier scale = 1 mm ÷ 10 = 0.1 mm
2. What is zero error in a vernier caliper? How many types are there?
• Define zero error.• When is zero error positive? When is it negative?
When jaws are closed, if the zero of the vernier scale does not coincide with the zero of the main scale, a zero error exists.
• Positive zero error: vernier zero is to the RIGHT of main scale zero.
• Negative zero error: vernier zero is to the LEFT of main scale zero.
Zero error must be corrected before taking any measurement.
• Positive zero error: vernier zero is to the RIGHT of main scale zero.
• Negative zero error: vernier zero is to the LEFT of main scale zero.
Zero error must be corrected before taking any measurement.
3. What are the steps to take measurement with a vernier caliper?
• How do you measure the diameter of a sphere with a vernier caliper?
Steps:
(i) Note the least count and correct any zero error.
(ii) Fix the object in the jaws and note the complete main scale divisions past the vernier zero — this is the main scale reading.
(iii) Find the vernier division that coincides with any main scale division — this is the vernier scale reading.
(iv) Total = Main scale reading + (Vernier reading × Least count).
(i) Note the least count and correct any zero error.
(ii) Fix the object in the jaws and note the complete main scale divisions past the vernier zero — this is the main scale reading.
(iii) Find the vernier division that coincides with any main scale division — this is the vernier scale reading.
(iv) Total = Main scale reading + (Vernier reading × Least count).
Screw Gauge
1. What is a screw gauge? Define pitch and least count.
• Define screw gauge, pitch, and least count.• How is the least count of a screw gauge calculated?
A screw gauge is a device used to measure a fraction of a smallest division on scale by rotating a circular scale over it.
Pitch = distance traveled by the circular scale in one rotation on the linear scale.
Pitch = distance traveled by the circular scale in one rotation on the linear scale.
Least Count = Pitch ÷ Total divisions on circular scale = 0.5 mm ÷ 50 = 0.01 mm
Parts: anvil, spindle, sleeve (linear scale), thimble (circular scale), datum line, and ratchet.2. What is the purpose of the ratchet in a screw gauge?
• Why is a ratchet used in a screw gauge?
The ratchet prevents the user from applying too much pressure on the object being measured. When the correct pressure is reached, the ratchet starts to click — this is the signal to stop turning and take the reading.
3. Compare the precision of metre rule, vernier caliper, and screw gauge.
• Which instrument is most precise and why?• Why can screw gauge give more precise readings than vernier caliper?
| Instrument | Least Count |
|---|---|
| Metre Rule | 1 mm |
| Vernier Caliper | 0.1 mm |
| Screw Gauge | 0.01 mm |
PART 4
Errors, Precision & Significant Figures
Errors in Measurement
1. What is an error? What are the two main types?
• Define error in measurement.• Name and define systematic and random errors.
Error is the uncertainty that arises during measurement. Every measurement, no matter how carefully taken, has some error — making all measurements only approximate.
Systematic errors: occur consistently in one direction (always + or always −). Sources: instrument imperfections, zero errors, wrong technique, personal bias. Reduced by: better instruments, improved technique.
Random errors: unpredictable, vary in magnitude and direction. Sources: fluctuations in conditions, reaction time. Reduced by: taking multiple readings and calculating the mean.
Systematic errors: occur consistently in one direction (always + or always −). Sources: instrument imperfections, zero errors, wrong technique, personal bias. Reduced by: better instruments, improved technique.
Random errors: unpredictable, vary in magnitude and direction. Sources: fluctuations in conditions, reaction time. Reduced by: taking multiple readings and calculating the mean.
2. What is a simple pendulum? How is its period measured accurately?
• Define period of a pendulum.• Why do we time 10 oscillations instead of 1?
A simple pendulum is a mass that swings back and forth about a fixed point. One oscillation = one complete swing back to the starting position and state of motion.
The period (T) = time for one complete oscillation. To reduce random error from human reaction time, we time 10 oscillations and divide by 10:
The period (T) = time for one complete oscillation. To reduce random error from human reaction time, we time 10 oscillations and divide by 10:
T = Total time for 10 oscillations ÷ 10
Precision and Accuracy
1. Differentiate between precision and accuracy.
• Define precision and accuracy.• Can a measurement be precise but not accurate? Give example.
Precision: degree of agreement between repeated measurements — how consistent results are (low scatter = high precision).
Accuracy: how close a measured value is to the true/accepted value — absence of systematic errors.
Example — darts at a target:
• Precise & Accurate: tightly grouped at bullseye.
• Precise, NOT Accurate: tightly grouped but off-center.
• Accurate, NOT Precise: near center but scattered.
• Neither: scattered and off-center.
Accuracy: how close a measured value is to the true/accepted value — absence of systematic errors.
Example — darts at a target:
• Precise & Accurate: tightly grouped at bullseye.
• Precise, NOT Accurate: tightly grouped but off-center.
• Accurate, NOT Precise: near center but scattered.
• Neither: scattered and off-center.
📝 Precision → consistency. Accuracy → closeness to truth. Both are needed for reliable measurements.
Significant Figures
1. What are significant figures? State the rules for identifying them.
• Define significant figures.• When are zeros significant?
All accurately known figures plus the first doubtful figure in a measurement are called significant figures. Rules:
1. All nonzero digits (1–9) are always significant.
2. Zeros between significant figures are significant (e.g., 100.8 → 4 sig. figs.).
3. In numbers >1, zeros used as place holders are NOT significant (e.g., 29,000 → only 2 sig. figs. unless written as 2.90 × 10⁴).
4. In numbers <1, leading zeros are NOT significant; zeros after a nonzero digit ARE (e.g., 0.0029 → 2 sig. figs., 0.00290 → 3 sig. figs.).
1. All nonzero digits (1–9) are always significant.
2. Zeros between significant figures are significant (e.g., 100.8 → 4 sig. figs.).
3. In numbers >1, zeros used as place holders are NOT significant (e.g., 29,000 → only 2 sig. figs. unless written as 2.90 × 10⁴).
4. In numbers <1, leading zeros are NOT significant; zeros after a nonzero digit ARE (e.g., 0.0029 → 2 sig. figs., 0.00290 → 3 sig. figs.).
2. What are the rules for rounding off numbers?
• How do you round off to 2 decimal places?• How do you round off to 3 significant figures?
Rule: Look at the digit to the right of the last digit you want to keep:
• If it is less than 5 → drop it (round down), previous digit unchanged.
• If it is 5 or greater → drop it and add 1 to the previous digit (round up).
Examples:
• 3.876 → 2 d.p. → 3.88 (6 ≥ 5, round up)
• 657.873 → 2 d.p. → 657.87 (3 < 5, round down)
• 24.68 → 3 sig. figs. → 24.7
• 0.07683 → 3 sig. figs. → 0.0768
• 7,847 → 3 sig. figs. → 7,850
• If it is less than 5 → drop it (round down), previous digit unchanged.
• If it is 5 or greater → drop it and add 1 to the previous digit (round up).
Examples:
• 3.876 → 2 d.p. → 3.88 (6 ≥ 5, round up)
• 657.873 → 2 d.p. → 657.87 (3 < 5, round down)
• 24.68 → 3 sig. figs. → 24.7
• 0.07683 → 3 sig. figs. → 0.0768
• 7,847 → 3 sig. figs. → 7,850
Key Vocabulary
Unit 1 Vocabulary
Important terms — learn these definitions for exam questions.
| Term | Definition |
|---|---|
| Physical quantity | Any quantity that can be measured (e.g., length, mass, time, temperature) |
| Non-physical quantity | A quantity that cannot be measured (e.g., taste, feeling, color) |
| Measurement | Comparison of an unknown physical quantity with a standard to determine its size |
| Unit | The standard with which a physical quantity is compared |
| Base quantity | One of the seven fundamental quantities from which all other quantities are derived |
| Derived quantity | A quantity obtained by multiplying or dividing base quantities (e.g., speed, area, force) |
| SI | Système International d'Units — the internationally accepted system of units with 7 base units |
| Scientific notation | Writing a number as mantissa × 10^exponent, where mantissa is ≥ 1 and < 10 |
| Mantissa | The decimal part in scientific notation, always greater than 1 and less than 10 |
| Prefix | A name given to a specific power of ten (e.g., kilo = 10³, milli = 10⁻³) |
| Scalar | A physical quantity described by magnitude only (e.g., mass, speed, temperature) |
| Vector | A physical quantity described by both magnitude and direction (e.g., force, velocity, displacement) |
| Resultant vector | A single vector representing the combined effect of two or more vectors |
| Least count | The minimum value that can be measured on a given instrument's scale |
| Vernier caliper | Instrument measuring fractions of a mm by sliding one scale over another; L.C. = 0.1 mm |
| Screw gauge | Instrument measuring fractions of a mm by rotating a circular scale; L.C. = 0.01 mm |
| Pitch | The distance the circular scale travels on the linear scale in one complete rotation of the screw gauge |
| Zero error | Error when the zero of vernier/circular scale does not coincide with zero of main scale when closed |
| Error | The uncertainty that arises in every measurement; all measurements are only approximate |
| Systematic error | Error that occurs consistently in one direction; caused by instrument faults, wrong technique, or bias |
| Random error | Unpredictable error varying in magnitude and direction; reduced by taking repeated readings |
| Precision | Degree of agreement between repeated measurements; how consistent results are |
| Accuracy | How close a measured value is to the true or accepted value |
| Significant figures | All accurately known digits plus the first doubtful digit in a measurement |
| Period (T) | Time taken for one complete oscillation of a pendulum |
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