Physics: Physical Quantities and Units

Physical Quantities, Units, and Measurement

• A physical quantity is a measurable property of a substance like length, time, mass or temperature
• Units are standard quantities for expressing physical quantities
• The International System of Units (SI Units) are used worldwide:
  • Length is measured in meters (m)
  • Mass is measured in kilograms (kg)
  • Time is measured in seconds (s)
  • Temperature is measured in Kelvin (K)
  • Electric current is measured in Amperes (A)
  • Amount of substance is measured in moles (mol)
  • Luminous intensity is measured in candela (cd)
• Derived units combine base units
  • Speed/velocity is measured in m/s
  • Acceleration is measured in m/s²
  • Force is measured in newtons (N), equivalent to kg·m/s²
  • Energy is measured in joules (J), equivalent to kg·m²/s²
• Rulers and calipers are used to measure length
• Balance scales measure mass
• Stopwatches measure time
• Thermometers measure temperature

Kinematics

• Kinematics is the study of motion without considering the forces that cause it
• Distance: Scalar quantity and represents the total path length traveled by an object
• Displacement: Vector quantity and represents the straight-line distance from start to end with direction
• Speed: Scalar quantity and is calculated as Distance/Time
• Velocity: Vector quantity and is calculated as Displacement/Time
• Acceleration: Rate of change of velocity, calculated as Δv/Δt, where Δv is the change in velocity and Δt is the time taken
• Equations of motion for constant acceleration:
  • v = u + at (v is final velocity, u is initial velocity, a is acceleration, t is time)
  • s = ut + (1/2)at² (s is displacement)
  • v² = u² + 2as

Dynamics

• Dynamics is the study of forces and their effects on motion
• Force: A push or pull that can cause an object to accelerate
• Newton's First Law of Motion: An object stays at rest or in uniform motion unless acted upon by an external force
• Newton's Second Law of Motion: Force equals mass times acceleration (F = ma)
• Newton's Third Law of Motion: For every action, there is an equal and opposite reaction
• Weight: The force of gravity on an object
  • Formula: W = mg (m is mass, g is acceleration due to gravity, approximately 9.8 m/s² on Earth)
• Friction: A force opposing motion between surfaces in contact
  • Static friction prevents an object from starting to move
  • Kinetic friction acts on a moving object
• Resultant Force: The single force with the same effect as all forces acting on an object

Mass, Weight, and Density

• Mass: The amount of matter in an object, measured in kilograms (kg), it is a scalar quantity
• Weight: The force exerted on an object due to gravity, measured in newtons (N), it is a vector quantity
  • W = mg (m is mass, g is gravitational acceleration)
• Density: Mass per unit volume, measured in kilograms per cubic meter (kg/m³)
  • ρ = m/V (ρ is density, m is mass, V is volume)

Pressure

• Pressure: Force applied per unit area
  • Formula: P = F/A (P is pressure, F is force, A is area)
  • Units of pressure: pascal (Pa), 1 Pa = 1 N/m²
• Atmospheric Pressure: The pressure exerted by the atmosphere's weight, approximately 1×10⁵ Pa at sea level
• Hydrostatic Pressure: The pressure exerted by a fluid at rest, dependent on fluid density, column height, and gravitational acceleration
  • Formula: P = ρgh (ρ is fluid density, g is gravitational acceleration, h is height)

Energy Stores and Energy Transfers

• Energy can be stored in different forms:
  • Kinetic Energy: The energy of motion
    • Formula: Ek = (1/2) mv² (m is mass, v is velocity)
  • Gravitational Potential Energy: Energy due to an object's position in a gravitational field
    • Formula: Ep = mgh (m is mass, g is acceleration due to gravity, h is height)
  • Elastic Potential Energy: Energy stored when stretching or compressing an object
    • Formula: E = (1/2) kx² (k is spring constant, x is displacement from equilibrium)
  • Chemical Energy: Stored in the bonds of atoms and molecules
  • Internal Energy: Total energy within a system, kinetic and potential
  • Thermal Energy: Internal energy associated with random particle motion
• Energy Transfers:
  • Work Done: Energy transferred when a force moves an object
    • Formula: W = Fd (F is force, d is distance moved)
  • Heat Transfer: Energy transferred due to temperature differences
    • Conduction: Energy transfer through a solid through particle collisions
    • Convection: Heat transfer in fluids via movement of fluid particles
    • Radiation: Energy transfer through electromagnetic waves

Kinetic Particle Model of Matter

• Kinetic Particle Theory: Matter is made of tiny particles in constant motion. Explains the properties of solids, liquids, and gases
• Solids:
  • Particles are closely packed and vibrate in fixed positions
  • Have strong intermolecular forces
  • Possess a fixed shape and volume
• Liquids:
  • Particles are close but can move past each other
  • Have weaker intermolecular forces than solids
  • Have a fixed volume, but take the shape of their container
• Gases:
  • Particles are far apart and move freely
  • Have very weak intermolecular forces
  • Have no fixed shape or volume, and expand to fill available space
• Temperature and Kinetic Energy:
  • The average kinetic energy of particles increases with temperature
  • Temperature is a measure of the average kinetic energy of particles
• Pressure of Gas:
  • Gas pressure results from collisions of gas particles with container walls
  • Increased temperature raises particle kinetic energy, leading to more frequent and forceful collisions, thus increasing pressure

Thermal Processes

• Heat: Energy transfer due to temperature difference from high to low temperature regions
• Specific Heat Capacity: Heat to raise the temperature of 1 kg of a substance by 1°C
  • Formula: Q = mcΔT (Q is heat, m is mass, c is specific heat capacity, ΔT is temperature change)
• Latent Heat: Heat to change a substance's state without changing temperature
• Latent Heat of Fusion: Heat to change a substance from solid to liquid
• Latent Heat of Vaporization: Heat to change a substance from liquid to gas
• Thermal Conductivity: How well a material conducts heat
  • Materials with high thermal conductivity, like metals, transfer heat efficiently
  • Materials with low conductivity, like wood or plastic, are good insulators
• Conduction, Convection, and Radiation: Three main methods of heat transfer
  • Conduction: Heat transfer through direct contact
  • Convection: Heat transfer in fluids via movement of fluid particles
  • Radiation: Heat transfer through electromagnetic waves

General Wave Properties

• Waves: Disturbances transferring energy through a medium (or space) without moving matter
• Types of Waves:
  • Transverse Waves: Particle displacement is perpendicular to wave travel direction (e.g., light, water waves)
  • Longitudinal Waves: Particle displacement is parallel to wave travel direction (e.g., sound, seismic waves)
• Key Properties of Waves:
  • Amplitude: Maximum displacement from rest position
  • Wavelength: Distance between two consecutive points in phase (crest to crest or trough to trough)
  • Frequency: Number of complete waves passing a point per second, measured in hertz (Hz)
  • Speed: Distance a wave travels per unit time
    • Formula: v = fλ (v is wave speed, f is frequency, λ is wavelength)
• Reflection: Wave bounces off a surface
• Refraction: Wave changes direction when passing from one medium to another
• Diffraction: Bending of waves around obstacles or through openings

Electromagnetic Spectrum

• Electromagnetic Waves: Waves not requiring a medium, propagating through a vacuum at the speed of light (3×10⁸ m/s)
• Electromagnetic Spectrum: Range of all types of electromagnetic radiation
  • Radio Waves: Used for communication (radio, TV)
  • Microwaves: Used in cooking and communication (mobile phones, satellite)
  • Infrared (IR): Emitted by warm objects, used in thermal imaging and remote controls
  • Visible Light: Light we can see, red (longer wavelength) to violet (shorter wavelength)
  • Ultraviolet (UV): Causes sunburns, used in sterilization
  • X-rays: Used in medical imaging
  • Gamma Rays: High-energy radiation for cancer treatment and produced by radioactive materials
• Properties of Electromagnetic Waves:
  • All travel at the same speed in a vacuum
  • All are transverse waves
  • Differ in wavelength and frequency

Light

• Light: Electromagnetic radiation visible to the human eye
  • It travels as transverse waves and through a vacuum
  • The speed of light in a vacuum is approximately 3×10⁸ m/s
• Reflection of Light:
• The angle of incidence equals the angle of reflection
• Reflection occurs when light bounces off a surface
• Refraction of Light:
  • It is the bending of light as it passes from one medium to another due to a change in speed
  • Refractive Index: Ratio of the speed of light in a vacuum to the speed of light in a medium
    • Formula: n = c/v (n is refractive index, c is the speed of light in a vacuum, v is the speed of light in the medium)
• Lenses
  • Convex Lenses: Converge light rays to a focal point
  • Concave Lenses: Diverge light rays
  • Focal length: The distance from the lens to the focal point
• Dispersion: Splitting of light into constituent colors (spectrum) when passing through a prism

Electric Charge

• Electric Charge: Property of matter causing it to experience force in an electric/magnetic field
  • Types of Charge: Positive and negative. Like charges repel, opposite charges attract
  • Coulomb's Law: Force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them
  • Formula: F = k (q1q2 / r²) (F is force, q1 and q2 are the charges, r is distance, k is Coulomb's constant)
• Charge Unit: coulomb (C), one electron's charge is approximately 1.6×10⁻¹⁹ C

Current of Electricity

• Electric Current: Flow of electric charge in a conductor, usually a wire
  • Unit: ampere (A)
  • Definition: 1 ampere is the flow of 1 coulomb of charge per second
  • Direction of Current: Conventional current direction is from the positive to the negative terminal
• Ohm's Law: Relates current, voltage, and resistance in an electrical circuit
  • Formula: V = IR (V is voltage, I is current, R is resistance)
  • Resistor: Limits the flow of electric current
• Electric Power: Rate at which electrical energy is consumed or produced
  • Formula: P = VI (P is power, V is voltage, I is current)

D.C. Circuits

• Direct Current (D.C.): Current that flows in one direction only, from positive to negative
  • The flow of charge in a D.C. circuit is constant
• Components of D.C. Circuits:
  • Battery: Provides the voltage that drives current
  • Resistor: Limits the flow of current
  • Switch: Opens or closes the circuit
  • Ammeter: Measures current
  • Voltmeter: Measures voltage across two points
• Series Circuits: Components are end-to-end; current is the same through all
  • Total resistance: Rtotal = R1 + R2 + …
  • Voltage is shared
• Parallel Circuits: Components connected across the same points; voltage is the same -Total resistance: 1/Rtotal = 1/R1 + 1/R2

Practical Electricity

• Electrical Energy: The energy supplied by a source of electricity, usually a battery or power supply
  • Formula for electrical energy: E = Pt (P is power (W) and t is time (s))
• Efficiency: The ratio of useful energy output to total energy input, expressed as a percentage
  • Efficiency = (Useful energy output / Total energy input) × 100%
• Electrical Safety:
  • Fuses: Protect circuits by breaking when current exceeds a limit
  • Circuit Breakers: Automatically break the circuit in the event of an overload or short circuit
  • Insulation: Rubber or plastic used to insulate electrical wires and prevent contact

Radioactivity

• Radioactivity: Process by which unstable atomic nuclei lose energy by emitting radiation
• Types of Radiation:
  • Alpha Radiation: Helium nuclei (2 protons, 2 neutrons), low penetration (stopped by paper/skin)
  • Beta Radiation: Fast-moving electrons (beta particles), moderate penetration (stopped by aluminum)
  • Gamma Radiation: Electromagnetic waves with high energy, high penetration (requires lead or concrete)
• Decay: Unstable nucleus transforms to a more stable one, emitting radiation
  • Alpha decay: Nucleus loses an alpha particle
  • Beta decay: Neutron becomes a proton, emitting an electron (beta particle)
  • Gamma decay: Nucleus releases excess energy as gamma radiation
• Half-life: Time for half of the radioactive atoms to decay
  • The half-life is constant for each radioactive isotope
• Uses of Radioactivity:
  • Medical Imaging: Radioactive isotopes used as tracers
  • Radiotherapy: Used to kill cancer cells
  • Carbon Dating: Determine age by measuring remaining carbon-14