PHD
  1. Classical mechanics  1.1. Newtonian mechanics  1.1.1. Laws of motion in Newtonian mechanics  1.1.2. Dynamics of particles and systems  1.1.3. Conservation laws  1.1.4. Central force motion  1.2. Lagrangian mechanics  1.2.1. Principle of minimum action  1.2.2. Euler–Lagrange equations  1.2.3. Constraints and normalized coordinates  1.2.4. Noether's theorem  1.3. Hamiltonian mechanics  1.3.1. Hamilton's equations  1.3.2. Canonical conversion  1.3.3. Poisson bracket  1.3.4. Action-angle variable  1.4. Rigid body mobility  1.4.1. Rotation of rigid bodies  1.4.2. Moment of inertia tensor  1.4.3. Euler's equations in rigid body dynamics  1.4.4. Gyroscopic motion  1.5. Chaos and nonlinear dynamics  1.5.1. Stage space and attractive  1.5.2. Bifurcation and chaos theory  1.5.3. Hamiltonian Chaos  1.5.4. Lyapunov exponent
  2. Electrodynamics  2.1. Maxwell's equations  2.1.1. Gauss's law for electricity  2.1.2. Gauss's law for magnetism  2.1.3. Faraday's Law  2.1.4. Ampere's Law  2.1.5. Boundary conditions in Maxwell's equations  2.2. Electromagnetic waves  2.2.1. Wave equation  2.2.2. Polarization  2.2.3. Reflection and Refraction  2.2.4. Waveguides and resonators  2.3. Special relativity  2.3.1. Lorentz transformations  2.3.2. Relativistic energy and momentum  2.3.3. Relativistic electrodynamics  2.3.4. Minkowski spacetime  2.4. Radiation and scattering  2.4.1. Dipole radiation  2.4.2. Multipole expansion  2.4.3. Compton scattering  2.4.4. Thomson and Rayleigh scattering  2.5. Plasma Physics  2.5.1. Debye Screening  2.5.2. Magnetohydrodynamics  2.5.3. Plasma instability  2.5.4. Fusion Plasma
  3. Quantum mechanics  3.1. Foundations of quantum mechanics  3.1.1. Principles of quantum mechanics  3.1.2. Wave function and probability interpretation  3.1.3. Uncertainty principle  3.1.4. Quantum Tunneling  3.2. Schrödinger Equation  3.2.1. Time-dependent Schrödinger equation  3.2.2. Time-independent Schrödinger equation  3.2.3. Eigenvalues and eigenfunctions in the Schrödinger equation  3.2.4. Path integrals in quantum mechanics  3.3. Quantum operators  3.3.1. Commutators and observables  3.3.2. Angular momentum operator  3.3.3. Ladder Operator  3.3.4. Pauli matrices  3.4. Quantum entanglement and measurement  3.4.1. Bell's theorem  3.4.2. Quantum Teleportation  3.4.3. Quantum entanglement and quantum decoherence in measurement  3.4.4. Quantum entanglement and measurement in quantum mechanics  3.5. Relativistic quantum mechanics  3.5.1. Klein–Gordon equation  3.5.2. Dirac equation  3.5.3. Quantum field theory  3.5.4. Feynman path integral
  4. Statistical mechanics and thermodynamics  4.1. Classical thermodynamics  4.1.1. Laws of Thermodynamics  4.1.2. Carnot cycle  4.1.3. Entropy and free energy  4.1.4. Thermodynamic efficiency  4.2. Kinetic theory of gases  4.2.1. Maxwell–Boltzmann distribution  4.2.2. Transport phenomenon  4.2.3. Mean free path  4.2.4. Non-equilibrium systems in the kinetic theory of gases  4.3. Statistical mechanics  4.3.1. Microstates and Macrostates  4.3.2. Partition function  4.3.3. Bose–Einstein and Fermi–Dirac statistics  4.3.4. Fluctuations and correlations  4.4. Phase transition  4.4.1. Important events  4.4.2. Landau theory  4.4.3. Ising model  4.4.4. Renormalization group theory
  5. Quantum field theory  5.1. Second Quantization  5.1.1. Quantum harmonic oscillator in second quantization  5.1.2. Creation and annihilation operators in second quantization  5.1.3. Path Integral in Second Quantization  5.1.4. Fock space  5.2. Quantum Electrodynamics  5.2.1. Feynman diagrams  5.2.2. Renormalization in quantum electrodynamics  5.2.3. Gauge invariance in quantum electrodynamics  5.2.4. Vacuum polarization  5.3. Quantum Chromodynamics  5.3.1. Quarks and gluons  5.3.2. Color range  5.3.3. Lattice QCD  5.3.4. Asymptotic freedom  5.4. Standard model of particle physics  5.4.1. Electroweak theory  5.4.2. Higgs mechanism  5.4.4. Grand Unified Theories
  6. General relativity and gravity  6.1. Einstein's field equations  6.1.1. Ricci tensor and scalar curvature  6.1.2. Schwarzschild solution  6.1.3. Kerr metric  6.1.4. Gravitational waves  6.2. Cosmology  6.2.1. Friedmann equation  6.2.2. Cosmic inflation  6.2.3. Dark matter and dark energy  6.2.4. Large scale structure  6.3. Black holes and wormholes  6.3.1. Event horizon in black holes and wormholes  6.3.2. Hawking radiation  6.3.3. Penrose process  6.3.4. Information paradox in black holes and wormholes
  7. Condensed matter physics  7.1. Crystal structure and lattice  7.1.1. Bravais lattices  7.1.2. Band theory in crystal structure and lattices  7.1.3. Phonons in crystal structure and lattice  7.1.4. Block's theorem  7.2. Superconductivity  7.2.1. BCS principle  7.2.2. Meissner effect  7.2.3. High Temperature Superconductor  7.2.4. Josephson effect

PHD → Classical mechanics → Newtonian mechanics ↓


Laws of motion in Newtonian mechanics


Newton's laws of motion are a set of three physical principles established by Sir Isaac Newton in the late 17th century. These laws form the foundation of classical mechanics and describe the motion of objects and their interaction with forces.

First law of motion: Law of inertia

The first law, called the law of inertia, states that an object will remain in its state of rest or in a straight line of uniform motion unless it is affected by an external force. In simple terms, things don't start moving, stop, or change direction unless something pushes or pulls them.

If F = 0, then a = 0 (where F is the net force and a is the acceleration).
If F = 0, then a = 0 (where F is the net force and a is the acceleration).

This can be understood with a simple example: a book lying on a table will stay where it is unless someone or something moves it. Another example is a hockey puck sliding on ice. If the ice is perfectly smooth and there is no friction, the puck will always slide in a straight line unless an external force, such as a hockey stick, changes its motion.

puck on ice

The practical observation of the first law would be while travelling in a car. If the car stops suddenly, the passengers will lean forward. This happens because the bodies of the passengers maintain their momentum due to inertia while the speed of the car changes.

Second law of motion: Law of acceleration

The second law gives us a quantitative description of force. It says that the force acting on an object is equal to the mass of that object multiplied by its acceleration. This is represented through the equation:

F = ma
F = ma

Where F is the applied force, m is the mass, and a is the acceleration. This law describes how the velocity of an object changes when an external force is applied to it. The greater the mass of the object being accelerated, the greater the amount of force required to accelerate that object.

Consider a car and a bicycle being pushed by applying the same amount of force. The bicycle has a greater acceleration than the car because of its smaller mass. This makes it clear that the greater the mass, the lesser will be the acceleration for the same amount of force.

Bicycle car the same force

The second law also explains scenarios such as lifting a heavy box: more force is needed to lift a lighter box than a heavier one. It also explains why a truck with a greater mass needs more fuel to achieve the same acceleration as a smaller vehicle.

Third law of motion: Action and reaction

The third law is famous for making this clear: "For every action, there is an equal and opposite reaction." This law asserts that forces always occur in pairs. If object A exerts a force on object B, then object B will exert an equal and opposite force on object A.

F AB = -F BA
F AB = -F BA

The most common example of this is when a person walks: as you push your foot backwards on the ground, the ground also pushes you forward with an equal force. Similarly, consider the reaction of a gun - a fast forward motion is met with an equal but slower backward motion.

force from the foot Response from the ground

The third law also applies in rocket flight. As the rocket pushes the exhaust gases backward, the gases push the rocket forward. This is fundamental to all types of propulsion systems.

Applications and implications

Newton's laws of motion apply to a wide variety of environments, from microscopic to cosmic scales, describing phenomena such as the orbits of planets. They form the basis for many other areas of physics and engineering.

Consider sports: when a football is kicked, the force applied results in acceleration according to the second law. The speed of the football, its direction and momentum change depending on the force of the kick, the wind and gravity.

In aerospace, these rules determine the design process for vehicles that depart the Earth's atmosphere, and are important in calculating fuel requirements, trajectories, and structural capabilities.

Limitations of Newtonian mechanics

Newton's laws, although very successful, have their limitations. They do not apply at very high speeds close to the speed of light or in strong gravitational fields. This led to the development of Einstein's theory of relativity which refined our understanding. Further, at the microscopic level where quantum effects dominate, classical mechanics is replaced by quantum mechanics.

Despite these limitations, Newton's laws remain incredibly useful. They provide accurate approximations in most everyday situations and are therefore indispensable in engineering, physics, and technology.

Conclusion

Newton's laws of motion fundamentally describe the relationship between the motion of objects and the forces acting on them. These laws have a profound influence in a variety of fields and set the stage for further advances in physics and science. From the simple act of walking to the complex trajectories of spacecraft, the legacy of Newton's laws endures and remains central to our understanding of the natural world.


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Laws of motion in Newtonian mechanics

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