SI units

General physics

Learning Objectives: Master the Fundamentals

Cambridge AS A Level Physics Curriculum (1.1 & 1.2):

1.1.1 Understand that all physical quantities consist of a numerical magnitude and a unit
1.1.2 Make reasonable estimates of physical quantities included within the syllabus
1.2.1 Recall the following SI base quantities and their units: mass (kg), length (m), time (s), current (A), temperature (K)
1.2.2 Express derived units as products or quotients of the SI base units and use the derived units for quantities listed in this syllabus as appropriate
1.2.3 Use SI base units to check the homogeneity of physical equations
1.2.4 Recall and use the following prefixes and their symbols to indicate decimal submultiples or multiples of both base and derived units: pico (p), nano (n), micro (μ), milli (m), centi (c), deci (d), kilo (k), mega (M), giga (G), tera (T)

Language Objectives: Build Scientific Communication Skills

Use appropriate scientific vocabulary when describing physical quantities and units
Express measurements using correct notation with numerical values and units
Communicate unit conversions and dimensional analysis clearly
Discuss the importance of standardized units in scientific communication
Apply proper pronunciation of SI prefixes and unit names

Key Terms: Essential Scientific Vocabulary

English Term	Russian Translation	Kazakh Translation
Physical Quantity	Физическая величина	Физикалық шама
Magnitude	Величина/Размер	Мөлшер
Unit	Единица измерения	Өлшем бірлігі
SI Base Unit	Основная единица СИ	ХБЖ негізгі бірлігі
Derived Unit	Производная единица	Туынды бірлік
Prefix	Приставка	Префикс
Dimensional Analysis	Размерностный анализ	Өлшемді талдау
Homogeneity	Однородность	Біртектілік
Standard	Стандарт	Стандарт
Measurement	Измерение	Өлшеу

Concept Cards: Visual Learning Tools

Physical Quantity

A physical quantity has two parts: Numerical Magnitude + Unit Example: 5.2 meters • 5.2 = numerical magnitude • meters = unit

SI Base Units

Remember LMTIT: • Length: meter (m) • Mass: kilogram (kg) • Time: second (s) • I (current): ampere (A) • Temperature: kelvin (K)

Prefixes Remember

Large to Small: Tera (T) → Giga (G) → Mega (M) → kilo (k) → BASE UNIT → deci (d) → centi (c) → milli (m) → micro (μ) → nano (n) → pico (p)

Glossary: Essential Definitions

Physical Quantity: A property of matter or physical phenomenon that can be measured and expressed as a numerical value multiplied by a unit.

Translation

Kazakh: Физикалық шама — заттың немесе физикалық құбылыстың өлшенетін және сандық мәнді өлшем бірлігіне көбейту арқылы өрнектелетін қасиеті.

Magnitude: The numerical value of a physical quantity, representing how many units are contained in the measurement.

Translation

Kazakh: Мөлшер — физикалық шаманың сандық мәні, өлшеуде неше бірлік бар екенін көрсетеді.

SI Base Unit: One of the seven fundamental units in the International System of Units (SI) from which all other units can be derived.

Translation

Kazakh: ХБЖ негізгі бірлігі — Халықаралық бірліктер жүйесіндегі (ХБЖ) жеті негізгі бірліктің бірі, олардан барлық басқа бірліктерді шығаруға болады.

Derived Unit: A unit that is expressed in terms of base units through mathematical relationships, such as area (m²) or velocity (m/s).

Translation

Kazakh: Туынды бірлік — математикалық қатынастар арқылы негізгі бірліктер тұрғысынан өрнектелетін бірлік, мысалы аудан (м²) немесе жылдамдық (м/с).

Prefix: A symbol placed before a unit to indicate a multiple or submultiple of that unit, making it easier to express very large or very small quantities.

Translation

Kazakh: Префикс — сол бірліктің еселігін немесе бөлшегін көрсету үшін бірліктің алдында қойылатын белгі, өте үлкен немесе өте кіші шамаларды өрнектеуді жеңілдетеді.

Dimensional Analysis: A method used to check equations and convert between units by analyzing the dimensions of physical quantities.

Translation

Kazakh: Өлшемді талдау — физикалық шамалардың өлшемдерін талдау арқылы теңдеулерді тексеру және бірліктерді түрлендіру үшін қолданылатын әдіс.

Homogeneity: The property of an equation where all terms have the same dimensions, ensuring the equation is physically meaningful.

Translation

Kazakh: Біртектілік — теңдеудің барлық мүшелерінің бірдей өлшемдері бар қасиеті, теңдеудің физикалық мағынасын қамтамасыз етеді.

Theory: Understanding Physical Quantities and Units

Explore more at Quizizz.

What are Physical Quantities?

Every measurement in physics consists of two essential parts: a numerical magnitude and a unit. For example, when we say «the length is 5.2 meters,» the number 5.2 is the magnitude, and «meters» is the unit.

Kazakh Translation

Физикадағы әрбір өлшеу екі маңызды бөліктен тұрады: сандық мөлшер және бірлік. Мысалы, «ұзындық 5,2 метр» деп айтқанда, 5,2 саны — мөлшер, ал «метр» — бірлік.

The International System of Units (SI)

The SI system is the modern form of the metric system and is the world’s most widely used system of measurement. It provides a standardized way for scientists worldwide to communicate measurements.

SI Base Quantities and Units

There are seven fundamental quantities in SI, but for AS Level Physics, we focus on five:

Base Quantity	Symbol	SI Unit	Unit Symbol
Length	l	meter	m
Mass	m	kilogram	kg
Time	t	second	s
Electric Current	I	ampere	A
Temperature	T	kelvin	K

Kazakh Translation

ХБЖ жүйесі — метрикалық жүйенің қазіргі заманғы түрі және әлемде ең кең қолданылатын өлшеу жүйесі. Ол әлем бойынша ғалымдарға өлшеулерді хабарласудың стандартталған тәсілін береді.

Derived Units

Derived units are formed by combining base units. They can be expressed as products or quotients of base units. Common Derived Units:

Area: m² (meter squared)
Volume: m³ (meter cubed)
Velocity: m/s or m s⁻¹
Acceleration: m/s² or m s⁻²
Force: N (newton) = kg⋅m⋅s⁻²
Energy: J (joule) = kg⋅m²⋅s⁻²

Kazakh Translation

Туынды бірліктер негізгі бірліктерді біріктіру арқылы құрылады. Олар негізгі бірліктердің көбейтіндісі немесе бөліндісі ретінде өрнектелуі мүмкін.

SI Prefixes

Prefixes are used to express multiples or submultiples of units, making it easier to work with very large or very small quantities.

Prefix	Symbol	Factor	Example
tera	T	10¹²	THz (terahertz)
giga	G	10⁹	GHz (gigahertz)
mega	M	10⁶	MHz (megahertz)
kilo	k	10³	km (kilometer)
deci	d	10⁻¹	dm (decimeter)
centi	c	10⁻²	cm (centimeter)
milli	m	10⁻³	mm (millimeter)
micro	μ	10⁻⁶	μm (micrometer)
nano	n	10⁻⁹	nm (nanometer)
pico	p	10⁻¹²	pm (picometer)

Dimensional Analysis and Homogeneity

Dimensional analysis is a powerful tool for checking the correctness of equations. For an equation to be physically meaningful, all terms must have the same dimensions. Example: In the equation v = u + at

v has dimensions [L T⁻¹]
u has dimensions [L T⁻¹]
at has dimensions [L T⁻²] × [T] = [L T⁻¹]

All terms have the same dimensions, so the equation is homogeneous.

Kazakh Translation

Өлшемді талдау теңдеулердің дұрыстығын тексерудің қуатты құралы. Теңдеудің физикалық мағынасы болу үшін барлық мүшелердің бірдей өлшемдері болуы керек.

Memory Exercise: Master the Terminology

Exercise 1: Complete the SI base units: 1. Length is measured in _______ (symbol: _____) 2. Mass is measured in _______ (symbol: _____) 3. Time is measured in _______ (symbol: _____) 4. Electric current is measured in _______ (symbol: _____) 5. Temperature is measured in _______ (symbol: _____)

Answer

1. meters (m) 2. kilograms (kg) 3. seconds (s) 4. amperes (A) 5. kelvins (K)

Exercise 2: Match the prefix to its factor: 1. nano (n) → a) 10⁶ 2. mega (M) → b) 10⁻⁹ 3. milli (m) → c) 10³ 4. kilo (k) → d) 10⁻³

Answer

1. nano (n) → b) 10⁻⁹ 2. mega (M) → a) 10⁶ 3. milli (m) → d) 10⁻³ 4. kilo (k) → c) 10³

Exercise 3: Identify base or derived units: 1. m/s² (acceleration) — ____________ 2. kg (mass) — ____________ 3. m² (area) — ____________ 4. A (current) — ____________

Answer

1. derived unit 2. base unit 3. derived unit 4. base unit

Worked Examples: Problem Solving Practice

Example 1: Unit Conversion

Problem: Convert 2.5 km to meters and to millimeters.

Solution

Solution: To meters: 2.5 km = 2.5 × 10³ m = 2500 m To millimeters: 2.5 km = 2.5 × 10³ m = 2.5 × 10³ × 10³ mm = 2.5 × 10⁶ mm = 2,500,000 mm

Pronunciation Guide

kilometer [ˈkɪləˌmiːtər] - километр meter [ˈmiːtər] - метр millimeter [ˈmɪləˌmiːtər] - миллиметр conversion [kənˈvɜːrʒən] - түрлендіру

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Example 2: Expressing Derived Units

Problem: Express the unit of force (newton) in terms of base SI units.

Solution

Solution: Force = mass × acceleration F = m × a Dimensions: • mass [M] → kg • acceleration [L T⁻²] → m s⁻² Therefore: Newton (N) = kg⋅m⋅s⁻² Answer: 1 N = 1 kg⋅m⋅s⁻²

Example 3: Dimensional Analysis

Problem: Check if the equation s = ut + ½at² is dimensionally correct.

Solution

Solution: Let’s check each term: Left side: s (displacement) has dimensions [L] Right side: • ut: [L T⁻¹] × [T] = [L] • ½at²: [L T⁻²] × [T²] = [L] All terms have dimensions [L], so the equation is dimensionally correct and homogeneous.

Example 4: Making Reasonable Estimates

Problem: Estimate the mass of a typical car and express it in appropriate SI units.

Solution

Solution: A typical family car has a mass of approximately 1000-1500 kg. Reasonable estimate: 1200 kg = 1.2 × 10³ kg Alternative expressions: • 1.2 Mg (megagrams) • 1,200,000 g • 1.2 tonnes

Interactive Investigation: Explore Unit Relationships

Investigation Questions:

Use the simulation to explore different unit conversions. How does changing the numerator affect the rate?
Create examples of derived units by combining different base quantities.
Practice converting between different prefixes using the interactive tools.

Investigation Answers

1. Changing the numerator scales the rate proportionally — doubling the numerator doubles the rate. 2. Examples: velocity (length/time), density (mass/volume), pressure (force/area) 3. Remember the factor relationships: kilo = 10³, milli = 10⁻³, etc. Move decimal point accordingly.

Collaborative Learning: Group Activity 1

Pair Work Instructions:

Work together to match SI units with their corresponding quantities
Discuss the logic behind each pairing with your partner
Take turns explaining why certain units are base units vs derived units
Quiz each other on prefix values and symbols

Collaborative Learning: Group Activity 2

Group Challenge Instructions:

Form teams of 3-4 students
Complete the interactive quiz on SI units and prefixes
Discuss each question as a team before answering
Compare your team’s performance with other groups
Review any concepts where your team scored lower

Individual Assessment: Test Your Mastery

Question 1: Which of the following is NOT a base SI unit? A) kilogram (kg) B) ampere (A) C) newton (N) D) second (s)

Answer

C) newton (N) Newton is a derived unit for force. It can be expressed as kg⋅m⋅s⁻² in terms of base units.

Question 2: Convert 3.2 × 10⁻⁴ m to millimeters. A) 3.2 × 10⁻¹ mm B) 3.2 × 10⁻⁷ mm C) 3.2 × 10⁻¹ mm D) 0.32 mm

Answer

D) 0.32 mm 3.2 × 10⁻⁴ m = 3.2 × 10⁻⁴ × 10³ mm = 3.2 × 10⁻¹ mm = 0.32 mm

Question 3: The unit of energy (joule) can be expressed in base SI units as: A) kg⋅m⋅s⁻² B) kg⋅m²⋅s⁻² C) kg⋅m⋅s⁻¹ D) kg²⋅m⋅s⁻²

Answer

B) kg⋅m²⋅s⁻² Energy = Force × Distance = (kg⋅m⋅s⁻²) × m = kg⋅m²⋅s⁻²

Question 4: Which prefix represents the factor 10⁻⁶? A) nano (n) B) micro (μ) C) pico (p) D) milli (m)

Answer

B) micro (μ) Micro (μ) represents 10⁻⁶. Remember: nano = 10⁻⁹, pico = 10⁻¹², milli = 10⁻³

Question 5: Check the dimensional homogeneity of the equation: E = ½mv² Where E is energy, m is mass, and v is velocity. Show that both sides have the same dimensions.

Answer

Solution: Left side (E — energy): [E] = [M L² T⁻²] Right side (½mv²): [m] = [M] [v²] = [L T⁻¹]² = [L² T⁻²] [mv²] = [M] × [L² T⁻²] = [M L² T⁻²] Both sides have dimensions [M L² T⁻²], so the equation is dimensionally homogeneous.

Question 6: A quantity has the dimensions [M L⁻¹ T⁻²]. What physical quantity could this represent? A) Force B) Pressure C) Energy D) Power

Answer

B) Pressure Pressure = Force/Area = [M L T⁻²]/[L²] = [M L⁻¹ T⁻²]

Question 7: Express 2.5 GW (gigawatts) in standard form using base SI units.

Answer

Solution: 2.5 GW = 2.5 × 10⁹ W Watt (W) = kg⋅m²⋅s⁻³ (in base units) Therefore: 2.5 GW = 2.5 × 10⁹ kg⋅m²⋅s⁻³

Additional Resources: Extend Your Learning

Recommended Websites:

Interactive Tools and Calculators:

Practice Materials:

Reflection: Consolidate Your Understanding

Take time to reflect on your learning journey:

Understanding Physical Quantities: Can you explain why both magnitude and units are essential for any measurement? □ I understand completely □ I need more practice □ I need help with this concept
SI Base Units Mastery: Can you recall all five base units (mass, length, time, current, temperature) and their symbols? □ Yes, I know them all □ I know most of them □ I need to memorize these better
Prefix Confidence: Rate your ability to convert between different SI prefixes (1-10): Large prefixes (kilo, mega, giga, tera): ___/10 Small prefixes (milli, micro, nano, pico): ___/10
Derived Units Understanding: Can you express derived units in terms of base units? Examples you’re confident with: ________________ Examples you need to practice: ________________
Dimensional Analysis Skills: Can you check if equations are dimensionally homogeneous? □ Yes, I can do this confidently □ I can do simple examples □ I need more practice with this
Real-world Applications: How will you use this knowledge in: • Laboratory experiments: ____________________ • Problem solving: ____________________ • Daily life: ____________________
Next Steps: What will you do to strengthen your understanding? □ Practice more unit conversions □ Memorize prefixes and their values □ Work on dimensional analysis problems □ Apply concepts to real-world situations □ Seek additional help or resources

Key Takeaway: Understanding units and measurements is the foundation of all physics. Master these concepts now, and they will serve you throughout your scientific journey! Remember the acronym LMTIT for base units: Length (m), Mass (kg), Time (s), I (current — A), Temperature (K)

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🎯 Learning Objectives: What will you learn?

Understand that all physical quantities consist of a numerical magnitude and a unit.
Make reasonable estimates of physical quantities included within the syllabus.
Recall the following SI base quantities and their units: mass (kg), length (m), time (s), current (A), temperature (K).
Express derived units as products or quotients of the SI base units and use the derived units for quantities listed in this syllabus as appropriate.
Use SI base units to check the homogeneity of physical equations.
Recall and use the following prefixes and their symbols: pico (p), nano (n), micro (μ), milli (m), centi (c), deci (d), kilo (k), mega (M), giga (G), tera (T).

🗣️ Language Objectives: How will you express your understanding?

Use key terms such as SI units, derived units, prefixes, and homogeneity in context.
Explain the difference between base and derived units using comparative structures.
Describe physical quantities using appropriate units and prefixes.

📘 Key Terms Table: Learn the vocabulary

Term (EN)	Translation (RU)	Translation (KZ)
Physical Quantity	Физическая величина	Физикалық шама
SI Unit	СИ единица	СИ бірлігі
Derived Unit	Производная единица	Туынды бірлік
Prefix	Префикс	Префикс
Homogeneity	Однородность	Біртектілік

🧠 Flashcards: Test yourself!

Physical Quantity: A measurable aspect of the physical world, such as length or mass.
SI Unit: The standard unit used to express a physical quantity.
Derived Unit: A unit that is a combination of base units.
Prefix: A symbol placed before a unit to indicate a multiple or fraction.
Homogeneity: The property of an equation where all terms have the same units.

📚 Glossary: Understand the concepts

Physical Quantity: A property of a material or system that can be quantified by measurement.
Translation
Физическая величина — это свойство, которое можно измерить. / Физикалық шама — өлшеуге болатын қасиет.
SI Unit: The internationally accepted unit for a physical quantity.
Translation
СИ единица — международно принятая единица измерения. / СИ бірлігі — халықаралық қабылданған өлшем бірлігі.
Derived Unit: A unit formed by combining base units.
Translation
Производная единица — это единица, образованная из базовых. / Туынды бірлік — негізгі бірліктерден құралған.
Prefix: A symbol that modifies the value of a unit by a power of ten.
Translation
Префикс — символ, изменяющий значение единицы. / Префикс — бірліктің мәнін ондық дәрежеге өзгерту үшін қолданылатын таңба.
Homogeneity: The condition where all terms in an equation have the same dimensional units.
Translation
Однородность — это когда все члены уравнения имеют одинаковые размерности. / Біртектілік — теңдеудегі барлық мүшелердің бірдей өлшем бірліктері болуы.

📝 Exercises: Memorize the key terms

Match the term with its definition: SI Unit, Derived Unit, Prefix, Homogeneity.
Fill in the blank: The SI unit of temperature is ______.
True or False: A derived unit is a base unit.

Answer

1. SI Unit → Standard unit; Derived Unit → Combination of base units; Prefix → Symbol for multiples; Homogeneity → Same units in equation. 2. Kelvin 3. False

🎥 Watch and Learn: Video on Physical Quantities and Units