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Learn Classical Mechanics

Predict how things move, from thrown balls to orbiting planets.

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Classical mechanics is the physics of motion for everyday objects, from a rolling ball to a planet in orbit. Newton's three laws and the conservation of energy, momentum and angular momentum let you predict where something will be and how fast it will move. It is the foundation every other branch of physics builds on and the first serious physics most people learn. You start with kinematics and free-body diagrams, then work toward rotation, oscillations and the more powerful Lagrangian approach. Learnr can turn this into a personal course of short, interactive lessons that adapt to your progress.

How to learn Classical Mechanics, step by step

Learn kinematics with graphs first. Read position, velocity and acceleration from graphs before using equations, since slopes and areas carry the meaning. Then solve projectile problems by treating horizontal and vertical motion separately, with only gravity acting vertically.
Draw a free-body diagram for every force problem. Isolate one object, draw every force acting on it and nothing else, then choose axes, tilted along the slope for an incline. Write Newton's second law along each axis. Most errors come from a missing or invented force.
Reach for conservation laws when forces get messy. If you only need speeds at two points, energy conservation is usually faster than forces. Use momentum conservation for collisions, and check whether kinetic energy is also conserved to tell elastic from inelastic.
Treat rotation as a parallel to linear motion. Map position, velocity, mass and force onto angle, angular velocity, moment of inertia and torque. Solve rolling-without-slipping problems, which combine both, and explain why a spinning skater speeds up when pulling in her arms.
Study oscillations and orbits. Derive the period of a mass on a spring and a small-angle pendulum, then apply Newton's law of gravitation to circular orbits. Simple harmonic motion returns in waves, circuits and quantum physics, so learn it well.
Work many problems, a few each day. Mechanics is learned through problems, not reading. A Learnr course with daily bite-sized sets and a streak builds the habit of setting up each problem the same careful way.

What you'll learn

Solve projectile and constant-acceleration problems with the kinematic equations
Draw free-body diagrams and apply Newton's second law, including friction and inclines
Use conservation of energy and momentum to analyze collisions and motion
Calculate torque, moment of inertia and angular momentum for rotating objects
Describe simple harmonic motion for springs and pendulums

What's inside your Classical Mechanics course

A sample path Learnr builds for Classical Mechanics. Your real course adapts to your goal and level.

1. Kinematics in one and two dimensions
2. Newton's laws and free-body diagrams
3. Work, energy and power
4. Momentum, impulse and collisions
5. Rotation, torque and angular momentum
6. Oscillations, gravitation and Lagrangian mechanics

How long does it take to learn Classical Mechanics?

An introductory mechanics course takes about 3 to 4 months at 4 to 6 hours a week, the same as a first physics semester. An intermediate course covering Lagrangian and Hamiltonian mechanics, central forces and rigid bodies is another semester and needs comfort with differential equations.

What you need before you start

Algebra and trigonometry for the introductory level, including vectors and components. A calculus-based course needs derivatives and integrals, and advanced mechanics needs differential equations.

Common mistakes to avoid

Thinking a moving object needs a force to keep it moving. Forces change velocity, so an object coasting at constant speed has zero net force.
Listing "the normal force" as always equal to weight. On an incline or in an accelerating elevator it is different, so find it from the free-body diagram.
Plugging numbers in too early. Solving symbolically first lets you check units and limiting cases before any arithmetic goes wrong.

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Classical Mechanics questions, answered

Is classical mechanics the same as Newtonian mechanics?

Newtonian mechanics is the core of it. Classical mechanics also includes the Lagrangian and Hamiltonian formulations, which describe the same physics using energy and are easier for complex systems.

Do I need calculus for classical mechanics?

An algebra-based course covers the main ideas without it. Calculus lets you handle changing forces and acceleration properly, and every university physics course uses it.

When does classical mechanics stop working?

It breaks down at speeds near the speed of light, where special relativity takes over, and at atomic scales, where quantum mechanics is needed. For everyday objects its predictions are extremely accurate.