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Classical Mechanics

via Brilliant

Overview

Here we'll establish the bedrock principles of physics and use them to reveal matter in motion; from drones and rockets to skyscrapers and blinking fireflies.

By the end, you'll develop a rigorous approach to describing the natural world and you'll be ready to take on new challenges in quantum mechanics and special relativity.

Syllabus

  • Introduction: A quick look at what classical mechanics can do for you.
    • Formula One Racing: Want to design the fastest car? You'll need classical mechanics for that.
    • Cellular Automaton: Complex behavior can emerge from very simple rules.
    • Huygens' Clock Puzzle: Get hands-on with interactive pendulums and crack this classic puzzle.
  • Kinematics: A common language for everything that moves.
    • Kinematics in the City: Navigate the difference between acceleration and velocity on the streets of the city.
    • The Kinematic Equations: Derive the most useful kinematic relationships for an accelerating object.
    • Angular Kinematics: Try your kinematics skills at the racetrack.
    • Projectile Motion: Can you help Robin Hood prove he's the best shot in Nottinghamshire?
    • Gene Expression Problem: Can you predict the number of proteins manufactured in a cell?
  • Newton's Laws: Three simple laws govern nearly everything you see.
    • What are Forces?: Ride on a park swing to learn the basics of forces.
    • The 3 Laws of Motion: Get to know Newton's laws of motion at hockey practice.
    • Weight and Scales: Use Newton's laws to help a fly escape from a sealed jar.
    • Pressure: Take a deep dive to learn about forces in fluids.
    • Buoyancy: How high can you fly in a hot-air balloon?
    • Drag Forces: Watch out! The air is stealing your energy.
    • Banked Curve Problem: How fast can you take a turn on a banked road?
  • Energy: It's the currency of the Universe.
    • Exploring Energy: Find out how energy transforms on the ski slopes.
    • Work-Energy Theorem: Uncover the work-energy theorem by taking an elephant for a sleigh ride.
    • Conservation of Energy: Energy can never be created or destroyed, only changed.
    • Power: How much energy do your muscles consume?
    • Elastic Energy: Can an inflated balloon store energy?
    • Potential Energy: How much work can be done by a compressed spring?
    • Drone Battery Problem: Find the right sized battery for your quadcopter.
  • Momentum: Solve some harder problems with a different angle on Newton's Laws.
    • Momentum in the Office: Annoy your coworkers by building a jet engine on your office chair.
    • Impulse-Momentum Theorem: Save your knees when you jump from trees.
    • Rocket Equation: How much fuel does a rocket need to get to space?
    • Ideal Gas Law: How many gas molecules are inside a basketball?
    • Photon Problem: Even particles of light have momentum and energy.
  • Reference Frames: To make measurements, first you'll need a coordinate system.
    • Relativity on the Train: Are you moving or am I?
    • Center of Mass Frame: Bumper car collisions are simple in this reference frame.
    • Rotating Frames: A rotating reference frame is necessary when you're driving around in circles.
    • Einstein's Theory of Relativity: The speed of light is constant in any reference frame.
  • Statics: The science of standing still.
    • Tower of Cards: Where is the weakest point in a tower of cards?
    • Irregular Towers: Derive the force on any single block in a stack.
    • Static Equilibrium: Two conditions must be satisfied for any building to stand tall.
    • Rope Statics: When you're scaling a cliff, it takes a lot of strength to stay still.
    • Body Statics: Which yoga poses require the most strength?
    • Plank Statics: Balance torque and internal forces while walking the plank.
  • Springs: In a mostly stable world, simple harmonic oscillations are the norm.
    • Energy Landscapes: A golf ball rolling in a valley behaves just like a spring.
    • Elastic Forces: Much of modern physics stems from a single force law.
    • Simple Harmonic Oscillators: A Florida orange moving around a circle is the perfect oscillator.
    • Pendulums: How can a pendulum clock keep good time?
    • Large-Angle Pendulum: Learn the basics of perturbation theory to tackle a more challenging pendulum.
  • Oscillations: You see new behaviors when you link oscillators together.
    • Vibrations in Molecules: The fingerprint of every molecule can be found in its vibrations.
    • Coupled Oscillations: Connect two pendulums by a spring, and let them talk.
    • Strings: Every possible vibration can be built up from simpler patterns.
    • Loaded Strings: Make waves by coupling oscillators in a line.
    • Firefly Problem: How do the flashes of fireflies in the night synchronize?
  • General Considerations: Where do we go from here?
    • Natural Units: Nature provides its own meter sticks, and it hints at the great unknown.
    • Lagrangian Mechanics: There's another way to understand all of mechanics, and it's awesome.

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