1.1.4

Scalar & Vector Quantities

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Scalar & Vector Quantities

A quantity is anything that can be measured, such as length, mass, or time. They can be divided into two groups: scalars and vectors.

What are quantities?

What are quantities?

  • Quantities are things we can measure.
    • Example: length, mass, force
  • Quantities can be divided into two groups:
    • Scalars
    • Vectors
  • The difference in scalars and vectors lies in whether the quantity has direction as well as size.
Scalar quantities

Scalar quantities

  • A scalar quantity has magnitude (size) only. They do not include direction.
    • Example: The mass of a ball is 2 kg (we do not need to know its direction).
  • Examples of scalar quantities:
    • Distance
    • Speed
    • Time
    • Mass
    • Energy
    • Temperature
Vector quantities

Vector quantities

  • A vector quantity has both magnitude and direction.
    • Example: A force of 10 N acting downwards.
  • Vectors are often represented by arrows.
    • The length of the arrow shows the size of vector (magnitude), and the direction it points shows the direction of vector.
  • Examples of vector quantities:
    • Force
    • Weight
    • Velocity
    • Acceleration
    • Momentum
    • Electric field strength
    • Gravitational field strength
Comparing scalars and vectors

Comparing scalars and vectors

  • Scalar = Magnitude only (e.g. “60 km/h”)
  • Vector = Magnitude + direction (e.g. “60 km/h north”)
  • Distance vs. Displacement:
    • Distance is a scalar (e.g. you walk 5 km).
    • Displacement is a vector (e.g. you are 5 km north of your starting point).
  • Speed vs. Velocity:
    • Speed is a scalar.
    • Velocity is a vector.
Jump to other topics
1

Motion, Forces & Energy

1.1

Physical Quantities & Measurement Techniques

1.1.1Measuring Length1.1.2Measuring Volume1.1.3Measuring Time1.1.4Scalar & Vector Quantities1.1.5Adding Vectors
1.2

Motion

1.2.1Average Speed1.2.2Calculating Average Speed1.2.3Velocity1.2.4Acceleration1.2.5Distance-Time Graphs1.2.6Speed-Time Graphs1.2.7More Speed-Time Graphs1.2.8Calculating Uniform Acceleration1.2.9Gravity1.2.10Free Fall - Distance-Time & Speed-Time Graphs1.2.11Air Resistance1.2.12Air Resistance - Graphs1.2.13Optional: Calculating Acceleration
1.3

Mass & Weight

1.3.1Mass1.3.2Weight1.3.3Gravity Calculations
1.4

Density

1.4.1Density1.4.2Equation for Density1.4.3Density - Experiments1.4.4Density - Calculations
1.5

Forces: Effects of Forces

1.5.1Spring Constant1.5.2Spring Constant Equation1.5.3Force & Acceleration1.5.4Friction
1.6

Forces: Turning Effects of Forces

1.6.1Circular Motion1.6.2Turning Effect1.6.3Moments1.6.4Calculating Moments
1.7

Forces: Centre of Gravity

1.7.1Equilibrium1.7.2Centre of Gravity1.7.3Centre of Gravity Experiment
1.8

Momentum

1.8.1Momentum
1.9

Energy, Work, & Power: Energy

1.9.1Energy Changes1.9.2Energy Conversion1.9.3Kinetic Energy Stored1.9.4Calculating Changes in Kinetic Energy1.9.5Gravitational Potential Energy Stored1.9.6Calculating Changes in GPE1.9.7Elastic Potential Energy Stored1.9.8Calculating Changes in EPE
1.10

Energy, Work & Power: Work

1.10.1Mechanical Work1.10.2Calculating Mechanical Work1.10.3Calculating Electrical Work Done
1.11

Energy, Work & Power: Energy Resources

1.11.1Energy Resources1.11.2Fossil Fuels1.11.3Geothermal Energy1.11.4Wind Energy1.11.5Water Energy1.11.6Tidal Energy1.11.7Nuclear Energy1.11.8Solar Energy1.11.9Original Source of Energy1.11.10Fusion1.11.11Efficiency1.11.12Calculating Efficiency1.11.13Energy Wastage
1.12

Energy, Work & Power: Power

1.12.1Power
1.13

Pressure

1.13.1Pressure1.13.2Atmospheric Pressure1.13.3Calculating Pressure1.13.4Liquid Pressure1.13.5Manometer1.13.6Calculating Liquid Pressure
2

Thermal Physics

2.1

Kinetic Particle Model of Matter

2.1.1Kinetic Particle Model of Matter2.1.2States of Matter2.1.3Properties of Gases
2.2

Thermal Properties & Temperature

2.2.1Thermal Expansion2.2.2Changes in Internal Energy2.2.3Heat Capacities2.2.4Heat Capacities Experiment2.2.5Internal Energy2.2.6Calculating Internal Energy2.2.7End of Topic Test - Thermal Physics2.2.8Changes of State2.2.9Evaporation2.2.10Factors Affecting Evaporation2.2.11Examples of Evaporation
2.3

Transfer of Thermal Energy

2.3.1Conduction2.3.2Molecular Conduction2.3.3Convection Currents2.3.4Radiation2.3.5Surface Colour2.3.6Emitting Radiation2.3.7Leslie's Cube & Other Radiation Experiments2.3.8Uses of Energy Transfer
3

Waves

3.1

General Properties of Waves

3.1.1Wave Basics3.1.2Transverse Wave3.1.3Longitudinal Wave3.1.4Ripple Tank3.1.5Wave Speed3.1.6Wave Speed Formula3.1.7Calculating Wave Speed3.1.8Wave Frequency3.1.9Calculating Wave Frequency3.1.10Wavelength3.1.11Diffraction
3.2

Light: Reflection & Refraction

3.2.1Reflection3.2.2Internal Reflection3.2.3Refraction3.2.4More Refraction3.2.5Refractive Index Equation3.2.6Refractive Index3.2.7Critical Angle3.2.8Optical Fibres3.2.9Optical Fibres in Communications3.2.10Medical Applications of Optical Fibres
3.3

Light: Thin Lenses

3.3.1Thin Converging Lenses 13.3.2Thin Converging Lens 23.3.3Thin Converging Lens 33.3.4Thin Converging Lens 43.3.5Calculating Lenses
3.4

Light: Dispersion of Light

3.4.1Dispersion of Light3.4.2Triangular Prisms 13.4.3Triangular Prisms 2
3.5

Electromagnetic Spectrum

3.5.1Properties of Electromagnetic Waves3.5.2Gamma Rays3.5.3X-Rays3.5.4UV Light3.5.5Visible Light3.5.6Infrared Radiation3.5.7Microwaves3.5.8Radio Waves3.5.9Other Uses of EM Waves3.5.10Analogue & Digital Signals
3.6

Sound

3.6.1Sound Waves3.6.2Ears3.6.3Speed of Sound3.6.4Measuring Sound Waves3.6.5Oscilloscope Traces3.6.6Sound Waves Experiment
4

Electricity & Magnetism

4.1

Simple Phenomena of Magnetism

4.1.1Magnets4.1.2Magnetic Forces4.1.3Magnetic Materials4.1.4Induced Magnetism4.1.5Temporary & Permanent Magnets4.1.6Electromagnets4.1.7Magnetic Field Lines
4.2

Electrical Quantities: Electric Charge

4.2.1Electrical Charge4.2.2Charged Objects4.2.3Static Electricity Experiments4.2.4Charging by Induction4.2.5Electric Fields4.2.6Electric Field Patterns4.2.7Conductors4.2.8Electrical Conductors - Electrons
4.3

Electrical Quantities: Electric Current

4.3.1Current4.3.2Conventional Current4.3.3Current Equation4.3.4Calculating Current4.3.5AC/DC
4.4

Electromotive Force & Potential Difference

4.4.1Electromotive Force4.4.2Potential Difference4.4.3Potential Difference Equation4.4.4Calculating Voltage
4.5

Electrical Quantities: Resistance

4.5.1Circuit Measurements4.5.2Resistance4.5.3Equation for Resistance4.5.4Measuring Resistance4.5.5Calculating Resistance & Ohm's Law4.5.6Variable Resistance4.5.7Resistance Graph
4.6

Electrical Energy & Electrical Power

4.6.1Electrical Work4.6.2Electrical Power4.6.3Calculating Electrical Work
4.7

Electric Circuits: Circuit Diagrams & Components

4.7.1Circuit Diagrams4.7.2Circuit Symbols4.7.3More Circuit Symbols4.7.4Diodes4.7.5LDRs & Thermistors
4.8

Electric Circuits: Series & Parallel Circuits

4.8.1Series Circuits4.8.2Series Circuits - Resistors4.8.3Series Circuits - Cells4.8.4Series Circuits - Potential Difference4.8.5Calculating Series Circuits4.8.6Parallel Circuits4.8.7Parallel Circuits - Current4.8.8Parallel Circuits - Resistance4.8.9Parallel Circuits in Practice
4.9

Electric Circuits: Action & Use

4.9.1Potentiometer4.9.2Potential Divider Equation
4.10

Electrical Safety

4.10.1Dangers of Electricity4.10.2Live & Neutral Wires4.10.3Earthing Metal Cases4.10.4Fuses & Trip Switches4.10.5Fuse Ratings
4.11

Electromagnetic Effects: Electromagnetic Induction

4.11.1Electromagnetic Induction4.11.2Size of e.m.f4.11.3Forces Between Electricity & Magnets4.11.4Rotation of Coil & Induced e.m.f
4.12

Electromagnetic Effects: The A.C. Generator

4.12.1The Rotating-Coil Generator4.12.2Features of a Rotating-Coil Generator
4.13

Magnetic Effect of a Current

4.13.1Magnetic Effect of a Current4.13.2Solenoid Field4.13.3Relays
4.14

Force on a Current-Carrying Conductor

4.14.1Magnetic Field Strength4.14.2Uses of Magnets & Currents4.14.3Catapult Experiment4.14.4Beam Force Experiment
4.15

Electromagnetic Effects: The D.C. Motor

4.15.1Motor Effect4.15.2Direction of Motor Effect4.15.3DC Motors4.15.4Coil of Wire in a Magnetic Field
4.16

Electromagnetic Effects: The Transformer

4.16.1Transformers4.16.2Transformers Equation4.16.3Types of Transformer4.16.4Principles of Transformer Operation4.16.5Energy in Transformers
5

Nuclear Physics

5.1

The Nuclear Model of the Atom

5.1.1Atomic Model5.1.2Scattering of Alpha Particles5.1.3Subatomic Particles5.1.4Proton & Nucleon Numbers5.1.5Calculating Number of Neutrons5.1.6Isotopes5.1.7More Isotopes5.1.8Carbon Nuclides5.1.9Nuclear Fusion5.1.10Nuclear Fission5.1.11More Nuclear Fission
5.2

Radioactivity: Detection of Radioactivity

5.2.1Radioactivity5.2.2Types of Radiation5.2.3Detection of Radioactivity5.2.4Background Radiation
5.3

Radioactivity: The Three Types of Nuclear Emission

5.3.1Three Types of Emission5.3.2Relative Ionising Effects5.3.3Electric Fields5.3.4Magnetic Fields Radiation
5.4

Radioactive Decay

5.4.1Radioactive Decay5.4.2Decay Equations5.4.3Half Life5.4.4Measuring Half-Life5.4.5Practical Applications of Radiation5.4.6Ionising Radiation5.4.7Safety Precautions
6

Space Physics

6.1

The Earth & the Solar System

6.1.1The Earth6.1.2The Moon6.1.3The Solar System & The Accretion Model6.1.4Gravitational Field & Speed of Light6.1.5The Sun's Gravitational Field
6.2

Stars & the Universe

6.2.1The Sun as a Star6.2.2Galaxies6.2.3Life Cycle of a Star like the Sun6.2.4Life Cycle of a Star Much Bigger than the Sun6.2.5Creation of Elements6.2.6Red-shift6.2.7The Big Bang6.2.8Cosmic Microwave Background Radiation6.2.9The Hubble Constant

Practice questions on Scalar & Vector Quantities

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  1. 1
    Which of the following is a scalar quantity?Multiple choice
  2. 2
    In a vector diagram, what does the direction of the arrow represent?Multiple choice
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Measuring Time

Adding Vectors