Amit & Deepali Sinha Foundation

Sinha Foundation Physics

Classical Mechanics

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

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  • 10lectures published
  • 4h 46mof video
  • 42lectures planned

Lectures

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Statics, Newton's laws, oscillations, energy and momentum conservation, central forces and orbits, 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 1Foundations

Arc playlist

Think Like a Physicist

Dimensional Analysis & Estimation18:00CC

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
Watch on YouTubeSlides (PDF, 5.4 MB)

The Art of Standing Still

Statics, Friction & Tension30:54CC

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
Watch on YouTubeSlides (PDF, 7.4 MB)

Torque and the Lever's Secret

Rotational Equilibrium & Center of Gravity28:53CC

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
Watch on YouTubeSlides (PDF, 6.1 MB)

F = ma, Properly

Newton's Laws & Free Body Diagrams31:15CC

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
Watch on YouTubeSlides (PDF, 6.8 MB)

Arc 2Motion & Oscillation

Arc playlist

Taming Differential Equations

Air Resistance & Terminal Velocity30:25CC

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
Watch on YouTubeSlides (PDF, 8.1 MB)

Projectiles and Polar Worlds

Motion in a Plane & Circular Motion30:11CC

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
Watch on YouTubeSlides (PDF, 7.1 MB)

The Universal Spring

Simple Harmonic Motion & Damped Oscillations31:09CC

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
Watch on YouTubeSlides (PDF, 8.6 MB)

Resonance

Driven Oscillations, Forced Vibration & Q Factor28:04CC

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
Watch on YouTubeSlides (PDF, 6.6 MB)

The Coupled Dance

Normal Modes, Beats & the Double Pendulum29:57CC

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
Watch on YouTubeSlides (PDF, 5.6 MB)

Arc 3Energy

Arc playlist

The Great Bookkeeper

Work, Kinetic & Potential Energy27:04CC

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
Watch on YouTubeSlides (PDF, 5.6 MB)

Coming Soon

New lectures weekly. Produced lectures may deviate from the plan, and each entry is replaced by the as-built record once it publishes. Updated August 29, 2026.

Arc 3EnergyArc playlist

L11

The Power of the Potential

Covers
Small oscillations via V″(x₀) · Taylor expansion at a minimum · effective spring constants · stability analysis as a universal tool
Problems
Frequency of small oscillations in V(x) = A/x² - B/x · diatomic molecule (Lennard-Jones), vibration frequency from the potential · cube balanced on a cylinder, stability criterion via energy curvature · ball in a cycloid trough, the isochronous oscillator
L12

Gravity, Shells, and Tides

Covers
Conservative forces in 3D · curl test · Newton's shell theorem (proved) · gravity inside the Earth · tidal forces as differential gravity
Problems
Tunnel through the Earth's center, the 42-minute train, completed · straight tunnel along any chord, same 42 minutes (the shocking part) · tides from the Moon vs the Sun, why the Moon wins despite being tiny · Roche limit estimate, when tides tear a moon apart · escape velocity vs orbital velocity, the √2 that rules spaceflight

Arc 4Momentum

L13

Momentum and the Rocket Equation

Covers
Momentum conservation from Newton's third law · variable-mass systems done correctly (F = dp/dt subtleties · Appendix E) · the rocket equation and its logarithmic cruelty
Problems
The rocket equation, why staging beats one big tank · sand leaking from a cart vs sand thrown from a cart, the crucial difference · freight car catching rain, momentum with growing mass · sand pouring onto a conveyor belt, the force, and where half the power goes · raindrop growing as it falls, acceleration g/7
L14

The CM Frame

Covers
Center-of-mass frame as the great simplifier · kinetic energy decomposition (KE of CM + KE about CM) · 1D elastic collisions by frame-hopping
Problems
Equal masses, why velocities simply exchange · basketball-tennis ball stack drop, the double-bounce launch · gravitational slingshot, stealing speed from a planet, via the planet's frame · maximum deflection angle when heavy hits light
L15

Collisions: Elastic and Otherwise

Covers
Elastic and inelastic collisions in 2D · invariants across collision types · inherently inelastic processes and where the energy goes
Problems
Equal-mass elastic collision in 2D, the guaranteed 90° opening angle · ballistic pendulum, where energy is lost and where it is not · chain piling on a table, why the scale reads three times the weight · bullet passing through two blocks in a row, sharing momentum and heat

Arc 5Least Action

L16

Least Action: Nature's Shortcut

Covers
The action · Euler-Lagrange equations derived · principle of stationary action · why L = T - V · equivalence with F = ma
Problems
Projectile via Lagrangian, recovering the parabola with no forces mentioned · Atwood machine via Lagrangian, one line instead of four FBDs · pendulum whose support slides freely on a rail · explicitly verifying stationarity for a thrown ball (perturbing the true path)
L17

Constraints Without Tears

Covers
Generalized coordinates · constraints eaten by coordinate choice · reading dynamics from the effective one-coordinate problem
Problems
Bead on a rotating hoop, revisited, L06's hard-won bifurcation in one Lagrangian line (the callback is the point , the hard way first, then the shortcut) · block sliding on a wedge that slides on ice · particle on a cone, two coordinates, gravity, and stability of circular motion · pendulum hanging from a cart free to roll, coupled coordinates tamed
L18

The Price of Constraint

Covers
Lagrange multipliers · extracting constraint forces · change of coordinates and what stays invariant
Problems
Particle sliding off a frictionless sphere, departure angle via multiplier · normal force on a bead on a curved wire, straight from the multiplier · cylinder rolling inside a larger cylinder, rolling constraint in action · disk on an incline, friction force recovered from the rolling multiplier
L19

Symmetry and Noether's Gift

Covers
Cyclic coordinates · conserved momenta · energy conservation from time symmetry · Noether's theorem, every symmetry buys a conservation law
Problems
Spherical pendulum, L_z conservation and the precessing orbit · particle on a helix, what is conserved and why · spring pendulum, which symmetries survive, which conservation laws follow · translation symmetry → momentum, the explicit Noether calculation

Arc 6Orbits

L20

The Effective Potential

Covers
Angular momentum conservation reduces 2D to 1D · effective potential V_eff = V + L²/2mr² · circular orbits and stability · classification of motion by energy
Problems
Stability of circular orbits in V ∝ rⁿ, the n > -3 rule · spiral death, capture in a 1/r³ force · apsidal precession of a nearly circular orbit · ISS orbit vs a thrown baseball, same physics, different energy line
L21

Kepler's Clockwork

Covers
Solving r(θ) · conic sections proved · Kepler's three laws derived
Problems
Halley's comet, aphelion from period plus perihelion alone · Hohmann transfer to Mars, the cheapest road in the solar system · a comet on a parabolic orbit, maximum time spent inside Earth's orbit · Kepler's third law by dimensional analysis, then honestly
L22

Two Bodies and Close Encounters

Covers
Reduced mass and the two-body problem · the CM + relative split · hyperbolic orbits · impact parameter and deflection angle · Rutherford scattering classically
Problems
Binary star masses from Doppler plus period · the Earth-Moon barycenter, both bodies orbit, and where the pivot really is · hyperbolic flyby, deflection angle vs impact parameter (the slingshot's geometry, done properly) · Rutherford scattering, closest approach and how an atom's emptiness was measured

Arc 7The Spinning World I

L23

Moment of Inertia: Mass That Matters Twice

Covers
L = Iω for planar objects · parallel and perpendicular axis theorems · computing I (stick · disk · sphere) · the scaling trick
Problems
I of a triangle by pure scaling argument (no integrals) · I of a Sierpinski-style fractal, the scaling trick at full power · rolling race, hoop vs disk vs sphere down an incline · meter stick as a physical pendulum, period and the center of oscillation · hollow vs solid sphere, telling them apart without cutting them open
L24

Torque: The Spin Equation

Covers
Τ = dL/dt and the three valid reference points (fixed point · CM · the subtle third case) · statics revisited as a special case
Problems
Falling chimney, why it snaps mid-fall, and where · cylinder on an incline, rolling vs slipping threshold · yo-yo, acceleration and tension on the way down · Atwood machine with a massive pulley, where the extra inertia hides
L25

Rolling Paradoxes

Covers
Rolling constraints in depth · contact-point subtleties · instantaneous axis of rotation
Problems
Spool pulled by thread at an angle, which way does it roll? (the flip angle) · ladder sliding down a frictionless wall, where it leaves the wall · ball rolling in a spherical bowl, SHM with the 7/5 correction · cylinder on an accelerating plank, rolling in a non-inertial setting
L26

Angular Collisions and the Sweet Spot

Covers
Angular impulse · angular momentum in collisions · center of percussion
Problems
Free rod struck at one end, instantaneous center of rotation · door and ball, where to hit so the hinge feels nothing (sweet spot) · pool ball struck at height 7R/5, immediate rolling, no skid · superball with backspin, the return-bounce reversal · person jumps onto a merry-go-round rim, angular momentum bookkeeping
L27

The Inertia Tensor Unveiled

Covers
Ω as a vector · general rotation = translation + rotation · the inertia tensor from first principles · why L need not be parallel to ω
Problems
Tilted rotating dumbbell, L visibly not parallel to ω · cube spinning about its space diagonal, computing L · bent rod rotating about one arm, the wobbling L vector · disk on a skewed axle, the bearing forces that shake the machine

Arc 8The Spinning World II

L28

Principal Axes

Covers
Principal axes (existence, Appendix F · diagonalization, Appendix G) · the two basic problem types, impulsive blows and torque-driven frequencies
Problems
Principal axes of a flat square plate · impulsive blow to a free rod in space, subsequent motion · skewed dumbbell on a spinning axle, torque frequency · balancing a car wheel, static vs dynamic imbalance, and why both matter
L29

Euler's Equations and the Tennis Racket

Covers
Euler's equations derived · torque-free motion · stability of rotation about principal axes · the intermediate axis theorem · free symmetric top from body and space frames
Problems
Tennis racket flip / Dzhanibekov effect, the full stability analysis · thrown plate wobble, proving the 2:1 ratio · football spiral, why prolate spin is stable · Chandler wobble, the Earth as a free symmetric top
L30

Gyroscopes: Defying Gravity

Covers
Euler angles · heavy symmetric top · precession (fast and slow) · nutation · gyroscope with θ̇ = 0
Problems
Bicycle wheel hanging from a string, precession instead of falling · toy top, fast-precession rate from τ = dL/dt · released top, nutation amplitude and the cycloid-like bob · precession of the equinoxes, the 26,000-year wobble estimated · why a sleeping top stands up, then eventually falls
L31

Fictitious but Felt

Covers
Transforming to accelerated frames · the four fictitious forces derived from one master equation · translation force · centrifugal force · equivalence principle preview
Problems
Plumb line on the rotating Earth, effective gravity vs true gravity · your weight at the equator vs the poles, two competing effects · rotating space station, artificial gravity design (radius, rim speed, Coriolis comfort) · water in a spinning bucket, deriving the paraboloid · helium balloon in an accelerating car, leans forward, and why that is deep
L32

The Coriolis World

Covers
Coriolis force · its two classic settings (motion on a carousel · projectiles on Earth) · azimuthal force · Foucault pendulum
Problems
Ball dropped from a tall tower, eastward deflection computed · hurricanes, why they spin opposite ways in the two hemispheres · long-range artillery, the correction that wins or loses a battle · Foucault pendulum, precession period at your latitude · the bathtub drain myth, why your sink does not care about the hemisphere

Arc 9Spacetime

L33

Simultaneity Shattered

Covers
The two postulates · relativity of simultaneity (the rear-clock-ahead rule) · time dilation from the light clock · muon decay as proof. (Qualitative paradoxes woven in from Appendix H.)
Problems
Einstein's train and the two lightning bolts, simultaneity broken cleanly · the light clock, time dilation in three lines · muon decay, reaching the ground on borrowed time · GPS, the daily clock drift with numbers
L34

Length Contraction and Lorentz

Covers
Length contraction derived · the Lorentz transformations from first principles · velocity addition · why nothing outruns light
Problems
Light clock lying along the motion, consistency forces length contraction · muon revisited, ground frame vs muon frame tell one consistent story · two rockets approaching at 0.9c each, what each sees · repeated small boosts, why velocities saturate at c (rapidity teaser)
L35

Paradoxes That Teach

Covers
Paradox anatomy, every SR paradox is a simultaneity error in disguise, rigid bodies cannot exist, leading vs trailing clocks
Problems
Pole-in-the-barn, resolved by simultaneity, not by tricks · the rivet and the hole, a "rigid body" paradox that kills rigidity · ladder falling into a grate, the 2D version, fully resolved · Bell's spaceship paradox, the string that breaks
L36

Spacetime: The Invariant Interval

Covers
The invariant interval as the true distance · causality and light cones · Minkowski diagrams · reading paradoxes off a diagram
Problems
Twin paradox on a Minkowski diagram, the asymmetry made visible · barn paradox replayed on the diagram, both stories at once · which event happened first? Frame-dependence of ordering, done concretely · the faster-than-light telephone, how FTL signaling breaks causality · proper time along competing worldlines, straightest path, longest time

Arc 10Relativistic Dynamics

L37

Doppler, Rapidity, and Relativity Without c

Covers
Longitudinal and transverse Doppler · rapidity, velocities add by adding angles · deriving relativity from symmetry alone (the deeper origin of c)
Problems
Redshift of a receding galaxy, relativistic Doppler with numbers · twin paradox by Doppler counting, each twin literally watches the other age · transverse Doppler, the pure time-dilation experiment (Ives-Stilwell) · ten successive boosts of 0.5c, rapidity turns multiplication into addition · the headlight effect, why relativistic sources beam forward
L38

E = γmc²: Energy Reborn

Covers
Relativistic momentum and energy motivated and derived · E² = p²c² + m²c⁴ · massless particles · transformations of E and p
Problems
Deuteron binding energy, weighing the mass defect · the Sun's mass loss, four million tons per second, from luminosity · photon rocket, the ultimate propulsion bound · Compton scattering, photon as a billiard ball · why pair production needs a nucleus nearby, conservation says no in vacuum
L39

Relativistic Collisions and Force

Covers
Collisions and decays via conservation of E and p · particle-physics units · force in relativity · relativistic rocket · what "mass" means (and why relativistic mass is retired)
Problems
Pion decay to muon plus neutrino, exact energy split · threshold energy for antiproton production, why the answer is 6mc², not 2mc² · collider vs fixed target, the quadratic advantage · decay opening angles, heavy particle decaying in flight · two masses joined by a relativistic string, tension and motion
L40

The 4-Vector Toolkit

Covers
4-vectors defined · the invariant inner product · velocity/momentum/force 4-vectors · why physical laws must be 4-vector equations
Problems
Velocity addition rederived in one line · invariant mass of a system, CM energy via the norm · photon 4-momentum, Doppler and aberration from one transformation · hyperbolic motion, constant proper acceleration solved exactly

Arc 11Gravity as Geometry

L41

Gravity as Geometry

Covers
Equivalence principle · gravitational time dilation from an accelerating rocket · redshift · first experimental tests
Problems
Pound-Rebka, measuring gravitational redshift over 22 meters · clocks on a mountain vs sea level, who ages faster and by how much · GPS grand finale, SR and GR corrections combined, signs and all · light bending by the Sun, the equivalence-principle estimate
L42

Horizons and the Longest Time

Covers
Uniformly accelerated frames · Rindler horizons · maximal proper time principle · twin paradox fully resolved (Appendix J synthesis) · series finale, mechanics as geometry
Problems
Constant-acceleration starship, reaching Andromeda within a human lifetime · the accelerating rocket's horizon, a black hole boundary without a black hole · twin paradox via maximal proper time, the final word · thrown ball as a geodesic, why free fall maximizes aging