Module 1: Measurements and Motion in 1D
✓ Complete
Module 2: Vectors and Motion in 2D/3D
In Progress
Module 3: Energy and Work
In Progress
Module 4: Center of Mass and Linear Momentum
In Progress
Module 5: Rotation and Equilibrium
✓ Complete
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1
M5L1 · Rotational Kinematics
✓ Built
Content Notes
- Intro: Linear↔rotational analogy scaffold (dark-blue 2-column table: all 3 kinematic equations + bridge equations v=rω, at=rα, ac=rω²). Central pedagogical spine carried forward through all M5 lessons.
- LOs: CC5.1 / LO5.1.1–5.1.5 — angular position, velocity, acceleration; constant-α kinematics; bridge to linear.
- Media: 3-tab vertical — angular quantities and the radian; constant-α equations and their linear analogs; bridge equations connecting rotation to linear motion at a point.
- Advanced Theory: 3-tab — why radians are dimensionless (arc length derivation); right-hand rule for angular vectors; unit conversions (rpm, rev/s, rad/s) with engineering context.
- Practice/Conceptual: dp-tabs-pills — Order Items (7 steps: solving constant-α problem); Sort Items (10 quantities → 3 buckets: angular only / linear only / both); Flip Cards (4 cards 2×2: radian definition, bridge equation direction, constant-α assumption, centripetal vs tangential).
- Practice/Computational: 5 accordion problems — unit conversion (rpm→rad/s), spin-up (find α and θ), braking (α from ω and t), bridge equations (find vt and ac at rim), CD/DVD engineering problem (max ω from material stress).
- Self-check: 5 questions bridging to M5L2 dynamics.
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2
M5L2 · Torque and Rotational Dynamics
✓ Built
Content Notes
- Intro: Archimedes lever quote. Analogy scaffold extended (adds F→τ, m→I, F=ma→τ=Iα, W=FΔx→W=τΔθ). Builds directly on M5L1 table with dynamics layer added.
- LOs: CC5.2 / LO5.2.1–5.2.6 — torque definition + cross product; moment of inertia as rotational mass; τ=Iα; parallel-axis theorem; rotational KE; rotational work-energy theorem.
- Media: 3-tab vertical — torque as the cause of angular acceleration (door hinge intuition, moment arm, sign convention); moment of inertia and why mass distribution matters; τ=Iα in multi-body problems + rotational KE and power.
- Advanced Theory: 3-tab — τ=r×F as a full cross product with right-hand rule + calculus connection (τ=dL/dt preview); deriving I=Σmr² from Newton's 2nd + parallel-axis theorem proof; moment of inertia reference table (7 objects) with cMR² shape-factor insight.
- Practice/Conceptual: dp-tabs-pills — Match Items (6 pairs: torque anatomy terms to definitions); Sort Items (8 changes → increases I / decreases I); Flip Cards (4 misconception cards: force vs torque, fixed I, net torque vs rotation, mass vs distribution).
- Practice/Computational: 6 accordion problems — wrench torque at 3 angles; disk α from τ=Iα + kinematic follow-through; solid disk vs hollow ring comparison (α ratio = 2:1); parallel-axis theorem verified two ways; flywheel KE + work-energy + average torque; Atwood machine with massive pulley (coupled linear+rotational).
- Self-check: 5 questions bridging to M5L3 rolling motion.
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3
M5L3 · Rolling Motion and Angular Momentum
✓ Built
Content Notes
- Intro: Two-part dark-blue framework box — Part 1: rolling constraint (vcm=Rω, total KE, static friction role, shape factor); Part 2: angular momentum (L=Iω, τ=dL/dt, conservation). Convergence lesson for all of M5.
- LOs: CC5.3 / LO5.3.1–5.3.7 — rolling constraint; total KE of rolling object; energy conservation on incline; incline race prediction from shape factor; L=Iω definition; angular impulse-momentum; conservation of L.
- Media: 3-tab vertical — rolling constraint and why contact point has zero velocity; incline race energy method and why shape beats mass; angular momentum definition, conservation, and applications.
- Advanced Theory: 3-tab — full incline race derivation showing M and R cancel, with 4-row shape-factor table (solid sphere fastest → hollow ring slowest) + sliding block comparison; angular momentum as full vector L=r×p, gyroscope precession, bicycle stability, 3D conservation, Noether's theorem connection; rolling friction (static vs kinetic), why static friction does no work, tire deformation insight.
- Practice/Conceptual: dp-tabs-pills — Order Items (7-step energy-method rolling procedure); Sort Items (6 skater actions → L same / increases / decreases, buckets empty); Flip Cards (4 cards: incline race winner + mass independence, skater ω increases but L conserved, KE partition for solid sphere, neutron star spin-up calculation).
- Practice/Computational: 5 accordion problems — cylinder down incline (speed + ω + KE split); three-way race (sphere vs cylinder vs ring, all numbers); figure skater tuck-in (conservation + KE increase source); stool + bicycle wheel flip (angular momentum transfer, spacecraft reaction wheel connection); hollow vs solid sphere up a ramp (hollow goes higher at same v).
- Self-check: 5 questions bridging to M5L4 static equilibrium.
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4
M5L4 · Static Equilibrium
✓ Built
Content Notes
- Intro: Le Ricolais quote. Dark-blue two-conditions framework box: ΣF=0 (translational) and Στ=0 (rotational) side by side, with pivot strategy callout box embedded — students see the central exam skill before they see a single equation.
- LOs: CC5.4 / LO5.4.1–5.4.6 — both conditions and why each is necessary; FBD construction for extended objects; pivot-point strategy; center of gravity location and role; beam/ladder/hinge/cable problems; tipping condition.
- Media: 3-tab vertical — why ΣF=0 alone is insufficient (couple example); pivot-point strategy step by step with beam+cable worked through (pivot at hinge eliminates both hinge components); ladders, center of gravity vs center of mass, and tipping condition.
- Advanced Theory: 3-tab — mathematical proof that pivot can be anywhere (ΣτB = ΣτA + d×ΣF) + statically indeterminate systems (3-legged stool vs 4-legged table); stable/unstable/neutral equilibrium table with CG-above-base criterion + engineering applications (cranes, sports cars, Leaning Tower); human body as lever system (forearm ×7 force amplification, neck, lower back, and why you lift with your legs).
- Practice/Conceptual: dp-tabs-pills — Order Items (7-step pivot strategy procedure); Sort Items (4-bucket: both conditions / ΣF=0 only / Στ=0 only / neither, buckets empty); Flip Cards (4 cards: ΣF=0 is sufficient misconception, pivot must be at center error, gravity anywhere on beam error, hinge exerts only vertical force error).
- Practice/Computational: 6 accordion problems — uniform beam+cable at 30° (pivot at hinge, find T then hinge components); non-uniform beam on two supports (CG given explicitly, verified with second pivot); ladder against frictionless wall (pivot at base, find Nw then μs,min); cantilever bracket hinge+cable (negative Fhy sign surprise explained); filing cabinet tipping (CG calculation, max drawer extension formula); human forearm holding textbook (bicep force ×10.5 the load, elbow joint compressive force).
- Self-check: 5 questions bridging to M5L5 elasticity (internal forces from equilibrium analysis drive the stress/strain calculations).
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5
M5L5 · Elasticity
✓ Built
Content Notes
- Intro: Hooke's 1678 quote. Bridge from M5L4 — equilibrium gives the forces; elasticity tells you what those forces do to real materials. Dark-blue three-panel framework box: tensile/compressive (Young's modulus), shear (shear modulus), and bulk (bulk modulus) — all three moduli shown side-by-side with stress/strain definitions and units.
- LOs: CC5.5 / LO5.5.1–5.5.6 — stress/strain definitions for all three deformation types; Hooke's law and elastic regime; Young's modulus formula ΔL = FL₀/(AY); shear modulus formula Δx = F∥L/(AS); bulk modulus formula ΔV = −(Δp/B)V₀; stress-strain curve interpretation from elastic limit through fracture.
- Media: 3-tab vertical — stress/strain/Young's modulus (thin vs thick wire, dimensionless strain, working formula, comparing Y for steel/bone/rubber); shear and bulk moduli (parallel-layer sliding, uniform compression, why liquids have no shear modulus, comparing B values); the stress-strain curve from elastic through yield/plastic deformation to fracture, ductile vs brittle, engineering safety factors.
- Advanced Theory: 3-tab — atomic origin of Hooke's law (Lennard-Jones potential, parabolic well at minimum, k = U''(r₀), universality of linear spring behavior for small displacements, connection to SHM); relationship between Y, S, and B via Poisson's ratio ν (S = Y/[2(1+ν)], B = Y/[3(1−2ν)], why S < Y always, seismic wave speed consequence); equilibrium+elasticity integration (cable tension from M5L4 → cable elongation, safety factor two-part check, thermal stress formula Y·α·ΔT, Tacoma Narrows Bridge resonance failure note).
- Practice/Conceptual: dp-tabs-pills — Match Items (6 pairs: tensile stress / tensile strain / Young's modulus / shear modulus / bulk modulus / elastic limit to their definitions); Sort Items (8 scenarios → Young's / shear / bulk modulus buckets, buckets empty); Flip Cards (4 cards 2×2: thick wire strength misconception, elastic ≠ stretchy, same stress different strain for steel vs aluminum, liquid incompressibility is approximate).
- Practice/Computational: 6 accordion problems — steel cable tension/strain/elongation + safety check (45.3 MPa, 4.53 mm over 20 m); femur bone compression under body weight (1.50 MPa, 40 μm compression, safety factor 113); rubber vibration isolator shear deformation (60 kPa, 2.0 mm, 5.7° shear angle); bulk compression of water at 50 atm (0.23% volume change, 4.6 mL, pressure for 1% = 217 atm); beam+cable combined problem (M5L4 equilibrium → T = 548.7 N → cable elongation 0.109 mm); material selection design problem (steel vs aluminum vs titanium under 3 simultaneous constraints — aluminum lightest at 1.93 kg, d = 30.1 mm).
- Module Synthesis: Dark-blue 5-step arc of Module 5 (M5L1–M5L5 described in sequence); self-check 5 questions (stress/strain/ΔL calculation, S < Y explanation, shear deformation in rubber pad, stress-strain curve labeling, beam cable elongation); bridge note to Module 6 oscillations (spring constant is the elastic modulus applied to SHM).
Module 6: Rotation and Torque
Not Started
Module 7: Gravitation and Oscillations
Not Started
Module 8: Fluids and Thermodynamics
Not Started