Units and Measurements in Physics

• Physics is the study of matter, energy, and the fundamental forces that govern the universe.
• Physics provides the foundation for understanding other natural sciences such as chemistry, biology, and earth science.

Units and Measurements

• Physical quantities are measurable quantities that describe the physical world.
• Fundamental quantities are the base quantities that do not depend on other quantities (e.g., length, mass, time, electric current, temperature, amount of substance, luminous intensity).
• Derived quantities are expressed in terms of fundamental quantities (e.g., area, volume, density, velocity, acceleration, force, energy, power).
• SI units (International System of Units) are the standard units for fundamental quantities:
  • Length: meter (m)
  • Mass: kilogram (kg)
  • Time: second (s)
  • Electric current: ampere (A)
  • Temperature: kelvin (K)
  • Amount of substance: mole (mol)
  • Luminous intensity: candela (cd)
• Dimensional analysis is the process of checking the relationship between physical quantities by identifying their dimensions.
• Accuracy refers to how close a measurement is to the true value.
• Precision refers to the repeatability of a measurement.
• Errors in measurement:
  • Systematic errors are consistent and repeatable errors.
  • Random errors are unpredictable and vary from measurement to measurement.

Motion in a Straight Line

• Distance is the total length of the path traveled by an object.
• Displacement is the change in position of an object in a specific direction.
• Speed is the rate at which an object covers distance.
• Velocity is the rate at which an object changes its displacement.
• Average speed is total distance traveled divided by total time taken.
• Average velocity is total displacement divided by total time taken.
• Instantaneous velocity is the velocity of an object at a particular instant in time.
• Acceleration is the rate of change of velocity.
• Uniform motion is motion with constant velocity (zero acceleration).
• Equations of motion for uniform acceleration:
  • v = u + at
  • s = ut + (1/2)at²
  • v² = u² + 2as
    • Where:
      • v = final velocity
      • u = initial velocity
      • a = acceleration
      • t = time
      • s = displacement
• Relative velocity is the velocity of an object with respect to another object.

Motion in a Plane

• Scalar quantities have magnitude only (e.g., speed, distance, mass, time).
• Vector quantities have both magnitude and direction (e.g., velocity, displacement, force, momentum).
• Vector addition:
  • Triangle law
  • Parallelogram law
• Vector resolution: splitting a vector into its components along specified axes.
• Projectile motion: motion of an object thrown into the air.
  • Horizontal component of velocity remains constant.
  • Vertical component of velocity changes due to gravity.
  • Time of flight: the total time the projectile is in the air.
  • Range: the horizontal distance covered by the projectile.
  • Maximum height: the highest vertical position reached by the projectile.
• Uniform circular motion: motion of an object moving at a constant speed along a circular path.
  • Centripetal acceleration: acceleration directed towards the center of the circle.
  • Centripetal force: the force that causes centripetal acceleration.
  • Angular velocity: the rate of change of angular displacement.
  • Angular acceleration: the rate of change of angular velocity.

Laws of Motion

• Newton's first law (law of inertia): An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an external force.
• Newton's second law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F = ma).
• Newton's third law: For every action, there is an equal and opposite reaction.
• Inertia is the tendency of an object to resist changes in its state of motion.
• Momentum is the product of an object's mass and velocity (p = mv).
• Impulse is the change in momentum of an object (Impulse = FΔt = Δp).
• Law of conservation of momentum: In the absence of external forces, the total momentum of a system remains constant.
• Friction is the force that opposes the motion of an object.
  • Static friction: the force that prevents an object from starting to move.
  • Kinetic friction: the force that opposes the motion of an object that is already moving.
• Rolling friction: the force that opposes the motion of an object rolling on a surface.

Work, Energy, and Power

• Work is done when a force causes a displacement (W = Fdcosθ).
• Energy is the capacity to do work.
• Kinetic energy is the energy of motion (KE = 1/2 mv²).
• Potential energy is stored energy:
  • Gravitational potential energy (PE = mgh)
  • Elastic potential energy (PE = 1/2 kx²)
• Work-energy theorem: The change in kinetic energy of an object is equal to the work done on it.
• Law of conservation of energy: Energy cannot be created or destroyed, but it can be transformed from one form to another.
• Power is the rate at which work is done or energy is transferred (P = W/t).
• Conservative forces are forces for which the work done is independent of the path taken (e.g., gravity, elastic force).
• Non-conservative forces are forces for which the work done depends on the path taken (e.g., friction).
• A collision is an event in which two or more objects exert forces on each other for a relatively short time.
  • Elastic collision: kinetic energy is conserved.
  • Inelastic collision: kinetic energy is not conserved.

System of Particles and Rotational Motion

• Center of mass: the point at which the entire mass of an object or system can be considered to be concentrated.
• Angular displacement: the angle through which an object rotates.
• Angular velocity: the rate of change of angular displacement.
• Angular acceleration: the rate of change of angular velocity.
• Torque: a force that causes rotation (τ = rFsinθ).
• Moment of inertia: a measure of an object's resistance to rotational motion (I = Σmr²).
• Kinetic energy of rotation (KE = 1/2 Iω²).
• Law of conservation of angular momentum: In the absence of external torques, the total angular momentum of a system remains constant.
• Rolling motion: a combination of translational and rotational motion.

Gravitation

• Newton's law of universal gravitation: Every object in the universe attracts every other object with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers (F = Gm1m2/r²).
• Gravitational constant (G = 6.674 × 10⁻¹¹ Nm²/kg²).
• Acceleration due to gravity (g) is the acceleration of an object due to the Earth's gravitational pull (approximately 9.8 m/s²).
• Gravitational potential energy (PE = -GMm/r).
• Escape velocity: the minimum velocity required for an object to escape the gravitational pull of a planet.
• Kepler's laws of planetary motion:
  • Law of orbits: All planets move in elliptical orbits with the Sun at one focus.
  • Law of areas: A line that connects a planet to the Sun sweeps out equal areas in equal times.
  • Law of periods: The square of the period of a planet's orbit is proportional to the cube of the semi-major axis of its orbit.
• Satellites: objects orbiting a planet.
  • Geostationary satellites: satellites that remain in the same position relative to the Earth's surface.

Mechanical Properties of Solids

• Elasticity is the ability of a solid to return to its original shape after being deformed.
• Stress is the force per unit area acting on a solid.
• Strain is the fractional deformation of a solid.
• Hooke's law: Stress is proportional to strain within the elastic limit.
• Young's modulus: a measure of a solid's stiffness (Y = stress/strain).
• Bulk modulus: a measure of a solid's resistance to compression (B = -P/(ΔV/V)).
• Shear modulus: a measure of a solid's resistance to shear stress (G = stress/strain).
• Poisson's ratio: the ratio of lateral strain to longitudinal strain.

Mechanical Properties of Fluids

• Pressure is the force per unit area exerted by a fluid (P = F/A).
• Pascal's law: Pressure applied to an enclosed fluid is transmitted equally to every point in the fluid.
• Buoyancy is the upward force exerted by a fluid on an object immersed in it.
• Archimedes' principle: The buoyant force on an object is equal to the weight of the fluid displaced by the object.
• Viscosity is a measure of a fluid's resistance to flow.
• Surface tension is the tendency of a liquid's surface to minimize its area.

Thermal Properties of Matter

• Temperature is a measure of the average kinetic energy of the molecules in a substance.
• Heat is the transfer of thermal energy from one object to another due to a temperature difference.
• Specific heat capacity is the amount of heat required to raise the temperature of 1 kg of a substance by 1 degree Celsius.
• Heat capacity is the amount of heat required to raise the temperature of an object by 1 degree Celsius.
• Change of state: the transformation of matter from one phase to another (e.g., solid to liquid, liquid to gas).
• Latent heat: the amount of heat required to change the state of a substance without changing its temperature.
• Thermal expansion: the tendency of matter to change in volume in response to changes in temperature.
  • Linear expansion
  • Area expansion
  • Volume expansion
• Conduction: heat transfer through a material by direct contact.
• Convection: heat transfer by the movement of fluids.
• Radiation: heat transfer by electromagnetic waves.

Thermodynamics

• Zeroth law of thermodynamics: If two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.
• First law of thermodynamics: The change in internal energy of a system is equal to the heat added to the system minus the work done by the system (ΔU = Q - W).
• Second law of thermodynamics: The entropy of an isolated system always increases or remains constant.
• Heat engine: a device that converts thermal energy into mechanical energy.
• Refrigerator: a device that transfers heat from a cold reservoir to a hot reservoir.
• Heat pump: a device that transfers heat from a cold reservoir to a hot reservoir, but is used for heating purposes.

Kinetic Theory

• Kinetic theory of gases: a model that explains the behavior of gases based on the motion of their molecules.
• Ideal gas law: PV = nRT
  • Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
• Average kinetic energy of a gas molecule is proportional to the absolute temperature.
• Root-mean-square (rms) velocity: the square root of the average of the squares of the velocities of the molecules.
• Degrees of freedom: the number of independent ways in which a molecule can possess energy.
• Law of equipartition of energy: Energy is equally distributed among all degrees of freedom.

Oscillations and Waves

• Simple harmonic motion (SHM): a periodic motion in which the restoring force is proportional to the displacement.
• Amplitude: the maximum displacement from the equilibrium position.
• Period: the time for one complete cycle of oscillation.
• Frequency: the number of cycles per unit time.
• Angular frequency: the rate of change of phase angle.
• Potential energy and kinetic energy in SHM.
• Damped oscillations: oscillations in which energy is lost over time.
• Forced oscillations: oscillations driven by an external force.
• Resonance: the phenomenon that occurs when the driving frequency is equal to the natural frequency of the system.
• Wave: a disturbance that travels through a medium, transferring energy without transferring matter.
• Transverse waves: waves in which the particles of the medium move perpendicular to the direction of the wave.
• Longitudinal waves: waves in which the particles of the medium move parallel to the direction of the wave.
• Wavelength: the distance between two consecutive crests or troughs of a wave.
• Wave speed: the speed at which a wave travels through a medium.
• Superposition of waves: the phenomenon that occurs when two or more waves overlap in the same region of space.
• Interference: the superposition of two or more waves that results in a new wave pattern.
  • Constructive interference: when waves add together to produce a larger amplitude.
  • Destructive interference: when waves cancel each other out to produce a smaller amplitude.
• Standing waves: waves that appear to be stationary.
• Beats: the periodic variation in amplitude that occurs when two waves of slightly different frequencies interfere.
• Doppler effect: the change in frequency of a wave due to the motion of the source or the observer.

Ray Optics and Optical Instruments

• Reflection: the bouncing back of light from a surface.
  • Laws of reflection:
    • The angle of incidence is equal to the angle of reflection.
    • The incident ray, the reflected ray, and the normal to the surface at the point of incidence all lie in the same plane.
• Refraction: the bending of light as it passes from one medium to another.
  • Snell's law: n1sinθ1 = n2sinθ2
    • Where n is the refractive index and θ is the angle of incidence or refraction.
• Total internal reflection: the phenomenon that occurs when light is incident on a boundary between two media at an angle greater than the critical angle.
• Lenses: transparent objects that refract light.
  • Convex lenses: converging lenses.
  • Concave lenses: diverging lenses.
• Lens formula: 1/f = 1/v - 1/u
  • Where f is the focal length, v is the image distance, and u is the object distance.
• Magnification: the ratio of the size of the image to the size of the object.
• Optical instruments: devices that use lenses and mirrors to form images (e.g., microscopes, telescopes).

Wave Optics

• Huygens' principle: Every point on a wavefront may be considered as a source of secondary spherical wavelets that spread out in the forward direction at the speed of the wave. The new wavefront is the envelope of these secondary wavelets.
• Interference of light waves: the superposition of two or more light waves that results in a new wave pattern.
  • Young's double-slit experiment: an experiment that demonstrates the interference of light waves.
• Diffraction: the bending of light waves as they pass around an obstacle or through an aperture.
• Polarization: the phenomenon in which the vibrations of a transverse wave are restricted to one plane.

Electric Charges and Fields

• Electric charge: a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field.
• Coulomb's law: The force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them (F = kq1q2/r²).
• Electric field: the region around an electric charge in which another charge would experience a force.
• Electric potential: the potential energy per unit charge at a point in an electric field.
• Electric dipole: a pair of equal and opposite charges separated by a small distance.
• Electric flux: a measure of the number of electric field lines passing through a surface.
• Gauss's law: The electric flux through any closed surface is proportional to the enclosed electric charge.

Electrostatic Potential and Capacitance

• Electrostatic potential: the potential energy per unit charge at a point in an electric field.
• Potential difference: the difference in electric potential between two points.
• Capacitance: the ability of a system to store electric charge.
• Capacitor: a device that stores electric charge.
• Parallel plate capacitor: a capacitor consisting of two parallel metal plates separated by a dielectric.
• Combination of capacitors:
  • Series combination
  • Parallel combination
• Energy stored in a capacitor.

Current Electricity

• Electric current: the rate of flow of electric charge.
• Ohm's law: The voltage across a conductor is proportional to the current flowing through it (V = IR).
• Resistance: the opposition to the flow of electric current.
• Resistivity: a measure of a material's resistance to the flow of electric current.
• Combination of resistors:
  • Series combination
  • Parallel combination
• Kirchhoff's laws:
  • Junction rule: The sum of the currents entering a junction is equal to the sum of the currents leaving the junction.
  • Loop rule: The sum of the voltage drops around any closed loop is equal to zero.
• Electrical power: the rate at which electrical energy is converted into other forms of energy (P = VI).
• Cells, EMF and internal resistance.

Moving Charges and Magnetism

• Magnetic field: the region around a magnet or a moving electric charge in which another magnet or moving charge would experience a force.
• Lorentz force: the force on a charged particle moving in a magnetic field (F = qvBsinθ).
• Motion of a charged particle in a magnetic field.
• Magnetic force on a current-carrying conductor.
• Torque on a current loop in a magnetic field.
• Moving coil galvanometer.
• Biot-Savart law: an equation that describes the magnetic field created by a current-carrying wire.
• Ampere's law: The line integral of the magnetic field around any closed loop is proportional to the current enclosed by the loop.
• Magnetic field due to a straight wire, a circular loop, and a solenoid.

Magnetism and Matter

• Magnetic dipole: a pair of equal and opposite magnetic poles separated by a small distance.
• Magnetic dipole moment: a measure of the strength and orientation of a magnetic dipole.
• Magnetization: the process of aligning the magnetic dipoles in a material.
• Magnetic intensity: a measure of the strength of an external magnetic field.
• Magnetic susceptibility: a measure of a material's ability to be magnetized.
• Types of magnetic materials:
  • Diamagnetic materials
  • Paramagnetic materials
  • Ferromagnetic materials
• Earth's magnetic field.

Electromagnetic Induction

• Electromagnetic induction: the production of an electromotive force (EMF) in a conductor when it is exposed to a changing magnetic field.
• Faraday's law of induction: The EMF induced in a closed loop is equal to the negative of the rate of change of the magnetic flux through the loop (EMF = -dΦ/dt).
• Lenz's law: The direction of the induced current is such that it opposes the change that produces it.
• Motional EMF: the EMF induced in a conductor moving in a magnetic field.
• Self-inductance: the property of a coil to oppose changes in the current flowing through it.
• Mutual inductance: the property of two coils to induce an EMF in each other.
• AC generator.

Alternating Current

• Alternating current (AC): an electric current that periodically reverses direction.
• Root-mean-square (rms) value of AC: the effective value of an alternating current or voltage.
• Reactance: the opposition to the flow of alternating current due to capacitance or inductance.
  • Inductive reactance
  • Capacitive reactance
• Impedance: the total opposition to the flow of alternating current in an AC circuit.
• Power in AC circuits.
• Transformers: devices that change the voltage of an alternating current.

Electromagnetic Waves

• Electromagnetic waves: waves that are created as a result of vibrations between an electric field and a magnetic field.
• Properties of electromagnetic waves:
  • They travel at the speed of light.
  • They are transverse waves.
  • They do not require a medium to travel.
• Electromagnetic spectrum: the range of all possible frequencies of electromagnetic radiation.
  • Radio waves
  • Microwaves
  • Infrared radiation
  • Visible light
  • Ultraviolet radiation
  • X-rays
  • Gamma rays

Dual Nature of Radiation and Matter

• Photoelectric effect: the emission of electrons from a metal surface when light shines on it.
• Einstein's photoelectric equation: E = hf - Φ
  • Where E is the kinetic energy of the emitted electrons, h is Planck's constant, f is the frequency of the light, and Φ is the work function of the metal.
• Wave-particle duality: the concept that light and matter have both wave-like and particle-like properties.
• de Broglie wavelength: the wavelength associated with a moving particle (λ = h/p).

Atoms

• Atomic models:
  • Thomson's model
  • Rutherford's model
  • Bohr's model
• Bohr's postulates:
  • Electrons revolve around the nucleus in specific orbits without emitting radiation.
  • The angular momentum of an electron is quantized.
  • Electrons can jump from one orbit to another by absorbing or emitting energy.
• Energy levels of hydrogen atom.
• Atomic spectra.

Nuclei

• Nuclear structure: the nucleus of an atom is made up of protons and neutrons.
• Nuclear size.
• Mass-energy relation: E = mc²
• Nuclear force: the force that holds the protons and neutrons together in the nucleus.
• Nuclear binding energy: the energy required to separate the nucleons in a nucleus.
• Nuclear fission: the splitting of a heavy nucleus into two or more lighter nuclei.
• Nuclear fusion: the combining of two or more light nuclei into a heavier nucleus.
• Radioactivity.

Semiconductor Electronics: Materials, Devices and Simple Circuits

• Semiconductors: materials that have a conductivity between that of a conductor and an insulator.
• Types of semiconductors:
  • Intrinsic semiconductors
  • Extrinsic semiconductors
• p-n junction: the junction between a p-type and an n-type semiconductor.
• Semiconductor diode: a device that allows current to flow in one direction only.
• Transistor: a semiconductor device used to amplify or switch electronic signals and electrical power.
• Logic gates: electronic circuits that perform logical operations.
• Integrated circuits.