Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate ↓


Classical mechanics


Classical mechanics is a branch of physics that deals with the motion of objects and the forces that act upon them. It forms the foundation for many advanced studies in physics and engineering. Initially developed by Isaac Newton and later refined by other physicists, classical mechanics describes how macroscopic objects behave under various forces. It includes several key concepts such as Newton's laws of momentum, energy, momentum, and angular momentum.

Newton's laws of motion

First law: Law of inertia

Newton's first law states that an object at rest stays at rest, and an object in motion continues to move in a straight line at a constant speed unless an external force is applied. This is called the law of inertia.

Second law: Law of acceleration

The second law states the relationship between the force applied to an object and its acceleration. It is expressed mathematically as follows:

F = ma

Where F is the force applied to the object, m is the mass of the object, and a is the acceleration.

Weight

The circle represents an object on which a downward force (weight) is acting due to gravity.

Third law: Action and reaction

Newton's third law states that for every action there is an equal and opposite reaction. This means that forces always come in pairs. If an object A exerts a force on an object B, then object B exerts an equal and opposite force on object A.

Example: When a swimmer pushes off from a pool wall, according to Newton's third law, the wall pushes the swimmer in the opposite direction with an equal force, causing the swimmer to move forward.

Concepts of force

Force is any interaction that changes the motion of an object without opposition. Forces can make objects speed up, slow down, stay in place, or change shape. The unit of force in the International System (SI) is the newton (N).

Work and energy

Work

Work is the energy transferred by a force moving an object over a distance. It is calculated as follows:

W = Fd cos theta

Where W is the work done, F is the force applied, d is the distance moved by the object, and theta is the angle between the direction of force and the direction of motion.

Kinetic energy

Kinetic energy is the energy that an object has due to its motion. It is given by the formula:

KE = frac{1}{2}mv^2

Where KE is the kinetic energy, m is the mass of the object, and v is its velocity.

Potential energy

Potential energy is the energy that is stored in an object due to its position in a force field, usually gravity. Gravitational potential energy is calculated as follows:

PE = mgh

Where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height above the reference point.

Conservation laws

Energy conservation

The principle of conservation of energy asserts that energy cannot be created or destroyed, but can only be converted from one form to another. The total energy in an isolated system remains constant.

Example: In a roller coaster, the total mechanical energy is conserved. At the highest point, the potential energy is maximum and the kinetic energy is minimum. On descent, the potential energy is converted into kinetic energy.

Conservation of momentum

Momentum is the product of the mass and velocity of an object. The law of conservation of momentum states that if no external force acts on a closed system, then its total momentum remains constant.

p = mv

Where p is momentum, m is mass, and v is velocity.

Example: In a collision, the momentum before collision is equal to the momentum after collision, provided there are no external forces interfering.

Collision

Elastic collision

In an elastic collision, both momentum and kinetic energy are conserved. Objects collide with each other without any deformation or heat generation.

Inelastic collision

In an inelastic collision, momentum is conserved, but kinetic energy is not. The objects may stick together or deform, causing the kinetic energy to be converted into other forms such as heat or sound.

Simple harmonic motion

Simple harmonic motion (SHM) is periodic motion where the restoring force is directly proportional to the displacement. An example of this is a mass attached to a spring.

F = -kx

Where F is the restoring force, k is the spring constant, and x is the displacement from equilibrium.

Mass

The blue circle represents a mass in simple harmonic motion on a spring.

Example: A pendulum swinging at small angles approximates simple harmonic motion because the forces involved satisfy the SHM criterion.

Angular velocity

Angular velocity and acceleration

Angular velocity is the rate of change of angular displacement and is measured in radians per second. Angular acceleration is the rate of change of angular velocity.

omega = frac{Delta theta}{Delta t}, alpha = frac{Delta omega}{Delta t}

Where omega is the angular velocity, Delta theta is the change in angle, Delta t is the change in time, and alpha is the angular acceleration.

Torque

Torque is a measure of the force that can rotate an object about an axis. It is a vector quantity, having both magnitude and direction.

tau = rF sin theta

Where tau is the torque, r is the lever arm distance, F is the applied force, and theta is the angle between the force and the lever arm.

Force

The above figure shows a lever arm rotating about a pivot point by applying a force at an angle.

Conservation of angular momentum

Angular momentum is preserved in a closed system with no external torque. The angular momentum of a rotating object is expressed as:

L = Iomega

Where L is the angular momentum, I is the moment of inertia, and omega is the angular velocity.

Example: An ice skater spinning with her arms outstretched will spin faster if she pulls her arms in, because angular momentum is conserved.

Applications in daily life

Classical mechanics can be seen in everyday activities and objects. From the basic act of walking, where our body muscles apply force to the ground, to driving a vehicle, where various forces and motions come into play.

Understanding classical mechanics helps design efficient machines, predict weather patterns, and even launch satellites into space by carefully calculating forces and motions.


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