Classical Mechanics

The complete undergraduate mechanics course, from statics to general relativity. Honors to olympiad level.

17lectures
5arcs
7h 56mof video
388problems worked

Part I: Statics to Kepler

Part I: statics, Newton's laws, oscillations, energy and momentum conservation, and orbits, ending on Kepler. Part II: least action, rigid-body rotation, non-inertial frames, and special and general relativity. Every lecture builds concept to fully solved problems, with limiting-case checks and a clear takeaway.

Slides are static snapshots. Each PDF is the final state of every slide. The animations, constructions, and step-by-step derivations happen in the video, so the slides are a reference to work alongside a lecture rather than a replacement for it. Free to download, adapt, and use in your own teaching under CC BY 4.0. Please keep the attribution.

Arc 1

Foundations

4 lectures · 1h 49mArc playlist

Dimensional Analysis, Estimation & Order of Magnitude

How did a photo leak an atomic secret?

YouTube Slides18:00CC

Covers: The physicist's toolkit · dimensions and the M-L-T system · the prediction recipe · Taylor expansions as the physicist's microscope · limiting cases as the thirty-second audit
Problems: The 1949 blast-yield estimate · why fleas out-jump athletes · the ant's strength secret · the fortunate mouse · the pendulum period without calculus · ocean-wave speed from thin air · Newton hiding inside Einstein · terminal velocity from dimensions · the tsunami capstone

Practice1.2 1.23 1.48 1.117

Statics, Friction, Tension, Normal Force & Capstan Equation

How do two turns of rope hold a ship?

YouTube Slides30:54CC

Covers: Force balance and equilibrium · the four workhorse forces, gravity, normal, tension, and friction · springs alone and in combination · the art of choosing clever axes
Problems: Block on an incline and the friction cone · the hanging sign on two ropes · why clotheslines sag · the best angle to drag a block · tension in a heavy rope · the capstan equation and why two turns of rope hold a ship

Practice1.63 1.64 1.67 1.103

Torque, Levers, Rotational Equilibrium & Center of Gravity

How far can a book stack lean?

YouTube Slides28:53CC

Covers: Torque and the turning strength · why any pivot works · the center of gravity · the tip-or-slip decision
Problems: The painter's plank · the leaning ladder · the tilting plane, tip against slide · the hanging chain and the catenary · stacking books to an infinite overhang

Practice1.234 1.235 1.236 1.237 1.271

Newton's Laws, Free Body Diagrams, Pulleys & Atwood Machine

How can 50 kg hold up 100 kg?

YouTube Slides31:15CC

Covers: Newton's three laws stated carefully · momentum as the deeper statement · the free-body diagram as a discipline · strings, pulleys, and constraints
Problems: The horse-cart paradox · the massless pulley · the block train · the painter's hoist and the factor of two · the double Atwood and its effective mass · block on a runaway wedge · the monkey and the counterweight

Practice1.72 1.73 1.74 1.78 1.82 See all 31

Arc 2

Motion & Oscillation

5 lectures · 2h 30mArc playlist

Air Resistance, Terminal Velocity & Differential Equations

Why doesn't rain fall like a bullet?

YouTube Slides30:25CC

Covers: F = ma read as a differential equation · the three doors, force as a function of time, velocity, or position · separation of variables · terminal velocity from force balance · the time constant, nature's own clock
Problems: A rocket's exponential burnout · the falling ball with linear drag · the coasting boat and Zeno's finite journey · why a thrown ball climbs faster than it falls · projectiles with drag and the vertical wall · the skydiver, quadratic drag, and the opening chute · the chain that feeds its own fall · five minutes of falling rain

Practice1.50 1.138 1.184 3.385 1.388 See all 62

Projectile Motion, Motion in a Plane & Circular Motion

Dropped or fired: which lands first?

YouTube Slides30:11CC

Covers: Motion split into independent stories · the trajectory equation and the range formula · polar coordinates and the frame that rides the motion · the four polar acceleration terms, centripetal and Coriolis among them
Problems: The dropped and fired bullets that land together · the monkey and the hunter · maximum range on a slope and the bisection insight · the parabola of safety · the cycloid and the wheel's still point · the bead on a spinning hoop and its bifurcation

Practice1.43 1.109 1.114 1.190 1.265 See all 90

Simple Harmonic Motion, Damped Oscillations & Pendulum

Why does one curve rule every wobble?

YouTube Slides31:09CC

Covers: The spring equation and its two-dial solution · simple harmonic motion hiding at every stable equilibrium · the pendulum linearized, then corrected · damping and its three fates, under, over, and critical
Problems: The spinning hoop's valley sings its note · a floating cylinder bobs on a liquid spring · liquid sloshing in a U-tube · the pendulum at large amplitude and the clockmaker's sixteenth · designing the perfect door closer · the 42-minute tunnel through the Earth

Practice1.50 1.109 1.110 1.131 1.299 See all 7

Resonance, Driven Oscillations, Forced Vibration & Q Factor

How can a steady note shatter a glass?

YouTube Slides28:04CC

Covers: The driven oscillator and its steady state · transients and why every launch is forgotten · the resonance curve and the ninety degree phase lag · the quality factor Q and its three faces
Problems: Amplitude and phase at resonance · stiffness-ruled and mass-ruled response, the two limits · tuning a car suspension against a rippled road · the wine glass, the marching bridges, and catastrophic resonance

Practice1.88 1.98 1.152 1.287

Normal Modes, Coupled Oscillators, Beats & Double Pendulum

Why does the swing come home?

YouTube Slides29:57CC

Covers: Two coupled oscillators and the handshake term · the normal modes and their private clocks · decoupling as a rotation of coordinates · beats, superposition, and the matrix form previewed
Problems: Two masses and three springs, both modes found · weakly coupled pendulums and the borrowed swing · the double pendulum from one analysis · the carbon dioxide molecule and the laser it powers · five beads and the language of vibration

Practice1.95 1.132 1.150 1.152

Arc 3

Energy

3 lectures · 1h 25mArc playlist

Work, Kinetic & Potential Energy, Conservation of Energy

Why does every track give one speed?

YouTube Slides27:04CC

Covers: Work as force through distance · the work-energy theorem · potential energy and the landscape picture · turning points and forbidden regions · stable and unstable equilibrium · the energy face of the quality factor Q
Problems: Three ramps, one arrival speed · the loop-the-loop and where the track lets go · the sliding chain solved in three lines · the three-g swing and its snapping rope · the spring drop and the overshoot factor of two · Galileo's peg pendulum and the hidden loop

Practice1.85 1.138 1.153 1.176 1.265 See all 118

Small Oscillations, Effective Spring Constant & Stability

Why is every valley the same curve?

YouTube Slides29:17CC

Covers: Taylor expansion at a stable minimum · the effective spring constant from curvature · a three-step recipe for small oscillations · the generalized inertia of a coordinate · stability analysis by curvature · the isochronous cycloid
Problems: Three landscapes under one magnifying glass · the hanging spring gravity cannot retune · the frequency of a power-law well · the vibrating molecule and its infrared clock · the cube balanced on a drum · the cycloid race that cannot be lost

Practice1.107 1.109 1.110 1.131 1.299 See all 6

Gravitation, Shell Theorem, Escape Velocity & Tidal Forces

Is gravity stronger inside the Earth?

YouTube Slides28:29CC

Covers: Conservative forces in three dimensions · the gravity well and the sign of E · Newton's shell theorem proved with one integral · gravity inside the Earth, a linear law · tides as the differences in the pull
Problems: The forty two minute tunnel train · every chord on one timetable · the Moon against the Sun · the Roche limit and Saturn's rings · escape velocity and the root two rule

Practice1.211 1.212 1.213 1.215 1.232 See all 11

Arc 4

Momentum

3 lectures · 1h 21mArc playlist

Conservation Laws, Rocket Equation & Variable Mass

What does a rocket push against?

YouTube Slides31:06CC

Covers: Momentum conservation derived from the third law · impulse and the isolated system · the variable mass law for mass that arrives or leaves · F = ma versus F = dp/dt settled · the rocket equation and its logarithm · the energy lost when mass merges
Problems: Why staging beats one big tank · leaking sand versus thrown sand · the freight car that slows in the rain · sand on a conveyor and the missing half of the power · the growing raindrop that falls at g over seven

Practice1.157 1.179 1.184 1.273 1.388 See all 19

Elastic Collisions & Gravitational Slingshot

Does a spinning hammer fly a parabola?

YouTube Slides27:10CC

Covers: The center of mass moves like one particle · the zero momentum frame · elastic collisions reverse every velocity in that frame · approach speed equals separation speed · Koenig's theorem, kinetic energy split into the center of mass part and the rest · the reduced mass of a two body oscillator
Problems: Newton's cradle and why equal masses swap velocities · the tennis ball on the basketball that launches at three times the speed · the tower of balls that reaches escape speed · fixed targets versus head on colliders · the gravitational slingshot and who pays for it

Practice1.153 1.160 1.171 1.265 1.267 See all 28

Inelastic Collisions, Ballistic Pendulum & Billiard Balls

Why do pool balls split at 90 degrees?

YouTube Slides22:43CC

Covers: Momentum survives every collision, kinetic energy only an elastic one · the velocity circle for collisions in the plane · Koenig's budget, the most energy a collision can lose · inherently inelastic processes and the momentum flux of arriving mass
Problems: Why two equal billiard balls always part at a right angle · how far a heavy ball can be knocked off its course · the ballistic pendulum and where its energy goes · a bullet through two blocks, equal momentum and three to one heat · the chain that presses three times its landed weight on a scale

Practice1.171 1.175 1.176 1.274 1.279 See all 29

Arc 5

Orbits

2 lectures · 52mArc playlist

Central Forces, Angular Momentum & Effective Potential

Why is one force law safe, one fatal?

YouTube Slides23:19CC

Covers: Two bodies become one body of reduced mass · a central force never changes the angular momentum · the sideways motion becomes a centrifugal wall, the effective potential · one energy line decides circle, wander, escape, or spiral in
Problems: Why circular orbits are stable only for forces weaker than the inverse cube · the planet that spirals in, infinitely many turns in a finite time · the pivot the Earth and the Moon share, and weighing Pluto and Charon with a clock · a thrown baseball is on an orbit too

Practice1.109 1.199 1.203 1.209 1.210 See all 9

Kepler's Laws, Orbits, Hohmann Transfer & Gravity Assist

How do you fly to Mars on the cheap?

YouTube Slides28:23CC

Covers: Trade time for angle: the orbit equation is an oscillator in the angle · every orbit is a conic, its eccentricity set by the energy · Kepler's three laws derived, equal areas from constant angular momentum and the period from the long axis alone
Problems: How far out Halley's comet goes, from its period alone · the cheapest road to Mars, two burns and a 259 day coast · how the aim sets the bend of a flyby past Jupiter · Rutherford's alphas and the size of the nucleus

Practice1.201 1.202 1.208 1.210 1.218 See all 7

388problems worked

Irodov, Part I: Mechanics

Every problem in the part, restated plainly and solved one step at a time.

Kinematics
Dynamics
Conservation Laws
Gravitation
Solid Bodies
Elasticity
Hydrodynamics
Relativistic Mechanics

Open Part I

Part II: Least Action to Relativity

Classical Mechanics II. Least action, rotation, and special and general relativity. 15 lectures in 3 arcs.

Arc 1Least Action3 lectures
Arc 2Rotation6 lectures
Arc 3Relativity and GR6 lectures