Classical Mechanics

The Science of Motion

Classical mechanics is the oldest and most developed branch of physics. It describes how objects move under the influence of forces. From a falling apple to a planet orbiting the sun, classical mechanics gives you the tools to predict and explain motion.

Newton's Laws

Isaac Newton's three laws of motion are the foundation of classical mechanics. The first law says that objects at rest stay at rest and objects in motion stay in motion unless acted upon by a net force. The second law says that force equals mass times acceleration: F = ma. The third law says that every force has an equal and opposite reaction.

These three laws, combined with Newton's law of universal gravitation, were revolutionary. They unified the motion of earthly objects with the motion of the planets into a single mathematical framework.

Energy and Work

Energy is conserved. This is one of the most powerful statements in all of physics. The work-energy theorem connects the work done on an object to its change in kinetic energy. Conservation of energy lets you solve problems without knowing the detailed path — only the endpoints matter.

Potential energy, kinetic energy, and the conversion between them are central to mechanics. Springs, pendulums, and orbits all involve energy transformations that conserve total mechanical energy.

Momentum

Linear momentum is also conserved when there are no external forces. This makes it invaluable for analyzing collisions and explosions. You will work through elastic and inelastic collisions and learn to use momentum conservation to find final velocities.

Rotation

Real objects rotate as well as translate. Angular velocity, angular acceleration, torque, and moment of inertia are the rotational analogs of their linear counterparts. Conservation of angular momentum explains why figure skaters spin faster when they pull their arms in.

Gravity

Newton's law of universal gravitation is an inverse-square law: the gravitational force between two masses decreases with the square of the distance between them. Kepler's three laws of planetary motion follow directly from this. You will derive them.

Oscillations

Simple harmonic motion — the oscillation of a mass on a spring or a pendulum at small angles — is ubiquitous in physics. You will find that the same differential equation describes many different physical systems and that its solution is a sinusoidal function.

Lagrangian Mechanics

At the end of this course, you will be introduced to a more powerful formulation of mechanics developed by Joseph-Louis Lagrange. Instead of forces, you work with energy. The Lagrangian approach is more general than Newton's, and it is the starting point for quantum mechanics and field theory.