Physics: Kinematics

• Physics is a natural science that involves the study of matter and its motion through space and time, along with related concepts such as energy and force

Mechanics

• Mechanics is the branch of physics dealing with the study of motion and forces.
• Kinematics describes motion without considering its causes.
• Dynamics is the study of the causes of motion, including forces and their effects.

Kinematics

• Displacement is the distance and direction of an object's change in position.
• Speed is the rate at which an object covers distance.
• Velocity is the rate of change of displacement (speed with direction).
• Acceleration is the rate of change of velocity.
• Equations of motion apply when acceleration is constant:
  • v = u + at
  • s = ut + (1/2)at²
  • v² = u² + 2as
  • s = (1/2)(u+v)t
• Projectile motion involves objects moving in two dimensions under the influence of gravity.
• Horizontal motion has constant velocity (if air resistance is negligible).
• Vertical motion has constant acceleration due to gravity (g ≈ 9.81 m/s²).

Dynamics

• Force: A force is a push or pull that can cause a change in an object's motion.
• Newton's First Law: 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 a force.
• Newton's Second Law: The force acting on an object is equal to the mass of the object times its acceleration (F = ma).
• Newton's Third Law: For every action, there is an equal and opposite reaction.
• Weight is the force of gravity acting on an object (W = mg, where g is the acceleration due to gravity).
• Friction is a force that opposes motion between surfaces in contact.
• Static friction prevents motion from starting.
• Kinetic friction acts on objects already in motion.

Momentum

• Momentum is the product of an object's mass and velocity (p = mv)
• Impulse is the change in momentum of an object (Impulse = Δp = FΔt).
• Conservation of Momentum: In a closed system, the total momentum remains constant if no external forces act.
• Elastic collision: Kinetic energy is conserved.
• Inelastic collision: Kinetic energy is not conserved.

Work, Energy, and Power

• Work is the energy transferred when a force causes displacement (W = Fdcosθ).
• Energy is the capacity to do work.
• Kinetic Energy (KE) is the energy of motion (KE = (1/2)mv²).
• Potential Energy (PE) is stored energy due to position or condition.
  • Gravitational Potential Energy (GPE) is the energy stored due to an object's height (GPE = mgh).
  • Elastic Potential Energy (EPE) is the energy stored in a deformed elastic object (EPE = (1/2)kx²).
• Power is the rate at which work is done or energy is transferred (P = W/t = Fv).
• Efficiency is the ratio of useful energy output to total energy input.

Materials

• Stress is the force per unit area acting on a material (stress = F/A).
• Strain is the fractional change in length of a material (strain = ΔL/L).
• Young's Modulus (E) is the ratio of stress to strain in the elastic region (E = stress/strain).
• Tensile stress is stress caused by a pulling force.
• Tensile strain is strain caused by a pulling force.
• Compressive stress is stress caused by a pushing force.
• Compressive strain is strain caused by a pushing force.
• Elastic deformation is reversible; the material returns to its original shape when the stress is removed.
• Plastic deformation is permanent; the material does not return to its original shape when the stress is removed.
• The limit of proportionality is the point beyond which stress is no longer proportional to strain.
• The elastic limit is the point beyond which deformation is no longer elastic.
• The yield point is the point at which the material begins to deform plastically with little or no increase in stress.
• Ultimate tensile strength (UTS) is the maximum stress a material can withstand before breaking.
• Breaking point is the point at which the material fractures.
• Hooke's Law states that the force needed to extend or compress a spring by some distance is proportional to that distance (F = kx, where k is the spring constant).

Waves

• A wave transfers energy without transferring matter.
• Transverse waves: Oscillations are perpendicular to the direction of energy transfer (e.g., light waves).
• Longitudinal waves: Oscillations are parallel to the direction of energy transfer (e.g., sound waves).
• Wavelength (λ) is the distance between two successive crests or troughs (or compressions or rarefactions).
• Frequency (f) is the number of complete oscillations per unit time (f = 1/T, where T is the period).
• Period (T) is the time taken for one complete oscillation.
• Amplitude (A) is the maximum displacement from the equilibrium position.
• Wave speed (v) is the speed at which the energy of the wave travels (v = fλ).
• Phase difference is the fraction of a cycle by which one wave leads or lags another.
• Superposition: When two or more waves overlap, the resultant displacement is the vector sum of the individual displacements.
• Constructive interference: Waves are in phase, resulting in a larger amplitude.
• Destructive interference: Waves are out of phase, resulting in a smaller amplitude or cancellation.
• Stationary waves (standing waves) are formed by the superposition of two identical waves traveling in opposite directions.
• Nodes are points of zero displacement.
• Antinodes are points of maximum displacement.
• Diffraction is the spreading of waves as they pass through an opening or around an obstacle.
• Refraction is the bending of waves as they pass from one medium to another due to a change in speed.
• Reflection is the bouncing back of waves when they hit a boundary.

Electromagnetic Waves

• Electromagnetic waves are transverse waves consisting of oscillating electric and magnetic fields.
• EM waves travel at the speed of light in a vacuum (c ≈ 3.00 x 10^8 m/s).
• The electromagnetic spectrum, in order of increasing frequency:
  • Radio waves
  • Microwaves
  • Infrared radiation
  • Visible light
  • Ultraviolet radiation
  • X-rays
  • Gamma rays
• Polarisation is the restriction of the vibrations of a transverse wave to one plane.

Electricity

• Electric charge is a fundamental property of matter.
• Coulomb's Law: The force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them (F = kq₁q₂/r²).
• Electric field is the region around a charged object where another charged object experiences a force.
• Electric field strength (E) is the force per unit positive charge (E = F/q).
• Electric potential (V) is the electric potential energy per unit charge.
• Potential difference (voltage) is the difference in electric potential between two points (V = W/q).
• Current (I) is the rate of flow of charge (I = ΔQ/Δt).
• Resistance (R) is the opposition to the flow of current (R = V/I).
• Ohm's Law states that the voltage across a conductor is directly proportional to the current through it, provided the temperature remains constant (V = IR).
• Resistivity (ρ) is a measure of a material's resistance to the flow of current (R = ρL/A).
• Power (P) in an electric circuit is the rate at which electrical energy is converted into other forms of energy (P = VI = I²R = V²/R).
• Series circuits: Components are connected end-to-end; the current is the same through all components; the total resistance is the sum of individual resistances.
• Parallel circuits: Components are connected side-by-side; the voltage is the same across all components; the total resistance is less than the smallest individual resistance.
• Kirchhoff's First Law (Junction Rule): The sum of the currents entering a junction equals the sum of the currents leaving the junction.
• Kirchhoff's Second Law (Loop Rule): The sum of the potential differences around any closed loop in a circuit is zero.

Quantum Physics

• Planck's constant (h) is a fundamental constant relating the energy of a photon to its frequency (h ≈ 6.63 x 10⁻³⁴ Js).
• The photoelectric effect is the emission of electrons from a metal surface when light shines on it.
• Einstein's photoelectric equation: E = hf = Φ + KE_max, where Φ is the work function of the metal.
• Work function (Φ) is the minimum energy required to remove an electron from the surface of a metal.
• Threshold frequency (f₀) is the minimum frequency of light required to cause the photoelectric effect.
• Wave-particle duality: Light and matter exhibit both wave-like and particle-like properties.
• De Broglie wavelength (λ) is the wavelength associated with a moving particle (λ = h/p = h/mv).
• Energy levels: Electrons in atoms can only occupy specific energy levels.
• The ground state is the lowest energy level of an atom.
• Excited states are energy levels higher than the ground state.
• Photons are emitted when electrons transition from higher to lower energy levels.
• Energy of emitted photon: E = hf = E₂ - E₁.

Nuclear Physics

• Atomic number (Z) is the number of protons in the nucleus.
• Mass number (A) is the total number of protons and neutrons in the nucleus.
• Isotopes are atoms of the same element with different numbers of neutrons.
• Strong nuclear force is the force that holds protons and neutrons together in the nucleus.
• Radioactive decay is the spontaneous breakdown of unstable nuclei.
• Alpha decay: Emission of an alpha particle (helium nucleus).
• Beta decay: Emission of a beta particle (electron or positron).
• Gamma decay: Emission of a gamma ray (high-energy photon).
• Half-life (T₁/₂) is the time taken for half of the radioactive nuclei in a sample to decay.
• Activity (A) is the rate of decay of radioactive nuclei (A = λN, where λ is the decay constant).
• Decay constant (λ) is the probability of decay per unit time (λ = ln(2)/T₁/₂).
• Nuclear fission is the splitting of a heavy nucleus into two smaller nuclei, releasing energy.
• Nuclear fusion is the combining of two light nuclei into a heavier nucleus, releasing energy.
• Mass defect is the difference between the mass of a nucleus and the sum of the masses of its individual nucleons.
• Binding energy is the energy required to separate a nucleus into its individual nucleons (E = mc², where m is the mass defect).

Explore kinematics, a branch of mechanics describing motion without considering its causes. Key concepts include displacement, speed, velocity, and acceleration. Learn the equations of motion and projectile motion principles.