Start with Newton
Learn Newton's three laws, free-body diagrams, kinematics equations, and energy conservation before adding more tools.
Classical Mechanics
Newton's laws, kinematics, energy, momentum, oscillations, and Lagrangian mechanics — the foundation of all physics.
What Is Classical Mechanics?
Classical mechanics is the branch of physics that describes the motion of macroscopic objects — from a thrown ball to a spacecraft orbit — using the laws formulated by Newton, Euler, Lagrange, and Hamilton. It operates in the regime where objects are much larger than atoms and move much slower than light, and it remains the workhorse of engineering, astronomy, and applied science.
The field divides naturally into kinematics (describing motion via position, velocity, and acceleration) and dynamics (explaining motion in terms of forces, masses, and energy). Newton's three laws of motion provide the classical starting point, while Lagrangian and Hamiltonian formulations offer powerful alternatives based on energy rather than force.
Core Concepts
Newton's Laws of Motion
Newton's first law (inertia) states that an object maintains its state of rest or uniform motion unless acted on by a net external force. The second law, F = ma, quantifies how force, mass, and acceleration relate. The third law — equal and opposite reactions — underpins everything from rocket propulsion to contact forces.
Conservation Laws
Classical mechanics is built around three conservation principles that hold whenever the corresponding symmetry is present:
- Conservation of momentum — holds when no net external force acts (Newton's third law applied to systems)
- Conservation of energy — kinetic and potential energy interconvert, with total mechanical energy conserved in closed conservative systems
- Conservation of angular momentum — governs rotating systems and orbital motion
Work and Energy
The work-energy theorem states that the net work done on an object equals its change in kinetic energy. Potential energy stores the capacity to do work — gravitational (mgh near Earth's surface), elastic (½kx²), and others. The concept of power, P = dW/dt, connects energy transfer to time.
Oscillations and Waves
Simple harmonic motion (SHM) arises whenever a restoring force is proportional to displacement. The pendulum, mass-spring system, and LC circuit all obey the same differential equation. Real oscillators experience damping; driven oscillators exhibit resonance, which is central to acoustics, engineering, and quantum mechanics.
Lagrangian and Hamiltonian Mechanics
The Lagrangian formulation replaces force vectors with scalar energy functions — L = T − V (kinetic minus potential energy). Euler-Lagrange equations then yield equations of motion automatically, even for complex constrained systems. The Hamiltonian formulation H = T + V reformulates mechanics in terms of generalised coordinates and momenta, bridging classical and quantum physics.
Learning Pathways
Add Momentum and Rotation
Extend to impulse-momentum, rotational dynamics, angular momentum, and the physics of oscillations and waves.
Analytical Mechanics
Master Lagrangian mechanics, constraints, Noether's theorem, the Hamiltonian formulation, and phase space.
Key Articles
Newton's Three Laws
A rigorous treatment of inertia, F = ma, and action-reaction pairs with worked examples.
Read →Conservation of Energy
Kinetic and potential energy, the work-energy theorem, and conservative vs non-conservative forces.
Read →Hooke's Law and Elasticity
Spring forces, elastic potential energy, and stress-strain behaviour in real materials.
Read →Resonance
Why resonant frequency matters in structures, circuits, and quantum systems.
Read →Laminar vs Turbulent Flow
Fluid mechanics fundamentals: Reynolds number, Bernoulli's principle, and viscosity.
Read →Noether's Theorem
The deep link between symmetry and conservation laws — the most important theorem in physics.
Read →Related Calculators
Frequently Asked Questions
What is the difference between kinematics and dynamics?
Kinematics describes motion (position, velocity, acceleration) without asking why it happens. Dynamics explains motion in terms of forces and masses.
When should I use Lagrangian mechanics?
When constraints make force analysis cumbersome, or when you want to exploit symmetry to find conserved quantities via Noether's theorem.
Is classical mechanics still relevant?
Yes — it governs engineering, aerospace, fluid dynamics, and robotics at scales far from atomic or relativistic extremes.
What is the work-energy theorem?
Net work done on an object equals its change in kinetic energy: W_net = ΔKE. This provides a scalar alternative to vector force analysis.