Mechanics

Laws of motion, forces, energy conservation, linear momentum, and system dynamics.

General idea of the topic

Mechanics studies the motion of bodies and the causes that produce or modify it. It starts from simple ideas, position, velocity, force, energy, and combines them into models that predict everything from the fall of a stone to the motion of the planets.

This block gathers the branches of classical mechanics in an order designed for study: first how motion is described, then why it happens, then the conservation laws of energy and momentum, and finally the topics that extend the framework: gravitation, oscillations, fluids and the analytical formulations.

What you will truly understand

By the end you will be able to describe the motion of particles and rigid bodies, set up and solve Newton's equations, use energy and momentum when they simplify the problem and recognize which model suits each situation.

You will also see how the different topics link together and how the same problem admits several paths.

Recommended learning route

1. Applications: simple machines and other situations where several concepts are combined.
2. Kinematics: rectilinear, circular, relative and two-dimensional motion.
3. Dynamics: Newton's laws, forces, equilibrium and motion of systems.
4. Rotation: rotation of rigid bodies, moment of a force, moment of inertia and angular momentum.
5. Work and Energy: work, power, kinetic and potential energy, and their conservation.
6. Linear Momentum: momentum, impulse and collisions.
7. Gravitation: law of gravitation, field, orbits and satellites.
8. Oscillations: harmonic motion, damping and resonance.
9. Fluids: fluids at rest and in motion, viscosity and waves.
10. Analytical Mechanics: Lagrange and Hamilton formulations.

Physical criterion you must acquire

The essential criterion is to choose the approach according to the question: kinematic if only the motion is described, dynamic if forces or accelerations are requested, energy if states are compared, and momentum if there are collisions or no external forces. All must give the same result when applied correctly.

Connection with real problems

• civil, mechanical and industrial engineering.
• sport, transport and safety.
• astronomy and space exploration.
• basis of modern physics and thermodynamics.

Final goal of the topic

The final goal is to master classical mechanics as a coherent set of models, choose the most suitable one in each case and justify its assumptions and results.