Mechanics · 100% marks notes

Method 01 · Dimension sieve first

Most wrong formulas die on dimensions alone; saves the 90-second budget for genuine physics.

Do this: Assign M,L,T (and I,θ if needed) to every symbol; kill options that fail homogeneity before algebra.

Method 02 · Log-diff error map

Turns every power and product into a linear percentage-error ledger without memorising cases.

Do this: Take ln of the computing formula, differentiate, replace d→δ and take absolute values.

Method 03 · Zero-error before formula

Systematic bias is not random; it shifts the measured value before propagation.

Do this: Correct every instrument reading for zero error, then apply least count; never correct the final answer instead.

Method 04 · Graph over single point

Reduces random scatter and matches how Advanced phrases pendulum-g, Ohm’s law and meter-bridge stems.

Do this: When multiple (x,y) pairs exist, extract slope/intercept matching the linearised law.

Dimensional consistency

Looks like: Check equation, find [X], or compare options by dimensions

Fast model: Write base dimensions for every symbol before algebra.

Error propagation

Looks like: Least count, % error, or combined measurement uncertainty

Fast model: Use relative-error addition with powers as multipliers.

Significant figures and rounding

Looks like: Report a computed result to correct precision

Fast model: Limit digits by the least precise measured input.

Named experiment setup

Looks like: Vernier, screw gauge, pendulum-g, Y, capillary, calorimeter, optics, resonance, Ohm/bridge

Fast model: Name what is measured and the working formula before numbers.

Method 01 · Component split stamp

Stops illegal use of level-ground T,H,R when launch height or landing height differs.

Do this: Before any ‘range formula’, write horizontal and vertical equations separately.

Method 02 · v–t area ledger

Handles direction changes without chaining wrong equations across breaks.

Do this: For piecewise 1D motion, sketch v(t); displacement is signed area.

Method 03 · Relative-vector triangle

Makes ‘velocity of rain wrt man’ a subtraction, not a new physical law.

Do this: Draw v_A, v_B and v_{A/B}; solve with components or geometry for rain angle / drift / min distance.

Method 04 · Circular kinematics gate

Prevents writing a=v²/r as the full acceleration when |v| changes.

Do this: Ask: is speed constant? If yes, only centripetal a; if speeding up, add tangential a_t=rα.

1D motion with piecewise acceleration

Looks like: Velocity–time or position with changing a

Fast model: Integrate piecewise; match v and x at junctions.

Projectile on level or incline

Looks like: Range, time of flight, max height, or landing on a slope

Fast model: Resolve g into axes tied to the ground or incline.

Relative velocity in 2D

Looks like: Rain–man, river–boat, or two-particle meeting

Fast model: Write vector relation v_rel = v_A − v_B before components.

Uniform circular / constrained path

Looks like: UCM speed, radial acceleration, or tangential change

Fast model: Separate tangential and radial; a_r = v²/ρ.

Method 01 · One-body-one-FBD

Internal string/friction forces cancel in the system equation but are needed for individual a and f.

Do this: Never merge two masses into one FBD until you know they share acceleration and you only need external forces.

Method 02 · Assume stick, then verify

Avoids guessing kinetic friction when the contact may not slip.

Do this: For static friction, assume common acceleration, solve f, then check |f|≤μ_s N.

Method 03 · Pseudo-force for accelerating supports

Converts constraint kinematics into statics or simple 1D motion.

Do this: When wedge/truck acceleration is given, shift to that frame, add −ma₀, then treat equilibrium or incline gravity+pseudo.

Method 04 · Constraint before algebra

Under-determined force equations become closed with geometry of string/wedge.

Do this: Write a₂=±a₁ or pulley string-length relations before solving ΣF.

Free-body multi-body system

Looks like: Blocks, strings, pulleys, or connected masses

Fast model: Draw one FBD per body; same magnitude for shared T and a when linked.

Friction threshold and motion

Looks like: Static/kinetic friction, impending motion, or incline

Fast model: Compare required friction with μN before assuming sliding.

Non-inertial frame pseudo-force

Looks like: Accelerating wedge, lift, or rotating frame (constant a)

Fast model: Add −ma_frame on every mass in the accelerating frame.

Constraint and string–pulley acceleration

Looks like: Movable pulley, wedge–block, or length constraint

Fast model: Differentiate the length constraint twice for a relations.

Method 01 · Energy ledger line

Prevents double-counting gravity both as work and as ΔU.

Do this: Write one line: K_i+U_i+W_nc=K_f+U_f (or equivalent) with every term named.

Method 02 · Constraint forces often do no work

Shrinks the ledger to gravity, spring and friction only in many track problems.

Do this: If displacement is perpendicular to N or along a fixed smooth surface constraint, drop that work.

Method 03 · Momentum then energy

Energy alone cannot find two unknown speeds after an inelastic split.

Do this: For explosion/collision plus later height, conserve momentum first (if allowed), then apply energy on each piece or COM frame.

Method 04 · F–x area for variable force

Avoids wrong average-force guesses.

Do this: When F(x) is graphed or piecewise, work is signed area under F_x–x.

Work–energy with variable force

Looks like: Spring, gravity, or F(x) along a path

Fast model: Use ΔK = W_all or ΔME = W_nonconservative.

Power and instantaneous rate

Looks like: P = F·v, average power, or engine–vehicle

Fast model: Use instantaneous P = F·v; average as ΔW/Δt.

Potential-energy landscape

Looks like: Stable points, escape, or turning points

Fast model: Set K=0 at turning points; use U(x) shape.

Conservative field test

Looks like: Path independence or find U from F

Fast model: Check curl F = 0 (2D/3D) or integrate F = −∇U.

Method 01 · COM as free particle

Decouples messy relative motion from the easy COM trajectory.

Do this: If ΣF_ext=0 horizontally, V_COM constant; solve internal motions relative to a steadily moving COM.

Method 02 · Impulse axis only

Walls and rough floors break momentum conservation in some components.

Do this: Conserve momentum only along directions with zero external impulse; apply e only along the contact normal.

Method 03 · COM-frame elastic flip

Replaces memorising both v₁,v₂ formulas under time pressure.

Do this: Transform to COM frame; for 1D elastic, reverse velocities; transform back.

Method 04 · e and momentum pair

Stops under-determined guessing from energy alone when e<1.

Do this: Always write two equations for two unknowns after 1D collision: Σp and e-definition.

Centre-of-mass kinematics

Looks like: System of particles, explosion, or variable mass pieces

Fast model: Track R_cm with M R_cm = Σ m_i r_i; F_ext = M a_cm.

1D elastic / inelastic collision

Looks like: Two masses collide; e given or perfectly elastic

Fast model: Use momentum + restitution (or energy if e=1).

Oblique collision and impulse

Looks like: Glancing blow, wall, or impulse J along normal

Fast model: Resolve into normal/tangential; impulse only along normal (smooth).

Variable-mass / rocket thrust

Looks like: Sand on conveyor, chain, or rocket equation idea

Fast model: Use thrust = u_rel (dm/dt) with careful mass-flow sign.

Method 01 · COM + spin split

One language covers rolling, toppling setup and free rigid collisions.

Do this: Always write translation of COM and rotation about COM as two coupled equations.

Method 02 · Torque point with zero impulse

Gives ω and V after impact without knowing friction impulse magnitude.

Do this: About the contact point during a quick collision on a rough surface, friction impulse may have no moment—use L conservation there if gravity impulse negligible.

Method 03 · Rolling friction audit

Same stick-then-verify discipline as linear friction—critical on Advanced rolling stems.

Do this: Assume pure rolling, solve f, verify |f|≤μN; if not, redo with kinetic friction and a≠rα.

Method 04 · Spool torque race

Predicts whether spool rolls toward or away from pull before full algebra.

Do this: For a pulled spool, take torque about contact point: pull line’s moment decides sense of roll tendency.

Moment of inertia and axis theorems

Looks like: I about a new axis, lamina, or composite body

Fast model: Build I from known pieces; then parallel/perpendicular axis.

Torque–angular acceleration

Looks like: Pure rotation about fixed axis

Fast model: Στ = Iα about the rotation axis.

Rolling without slipping

Looks like: Sphere/cylinder/hoop on rough surface

Fast model: Use a = Rα and static friction ≤ μN; energy if no slip throughout.

Angular momentum conservation

Looks like: Collision with rod, person on disc, or impulsive torque-free

Fast model: Conserve L about a fixed/CM axis when external impulse torque is zero.

Method 01 · Equilibrium shift first

Constant forces only shift the mean; ω still √(k/m).

Do this: For vertical springs or extra constant forces, find new equilibrium, then displace from there.

Method 02 · k_eff assembly

Converts cluttered spring diagrams into a single SHM constant.

Do this: Series/parallel springs → one k_eff; then ω=√(k_eff/m).

Method 03 · Force-law linearisation

Shows when motion is approximately SHM and gives ω without memorising every formula.

Do this: For pendulum, floating body, U-tube: expand restoring force to first order in displacement.

Method 04 · Phase portrait check

Kills wrong multi-correct statements about simultaneous maxima.

Do this: Remember x and v are π/2 out of phase; a and x are π out of phase.

Standard SHM identification

Looks like: x = A sin(ωt+φ) from force or energy

Fast model: Reduce to ẍ + ω²x = 0; read ω.

Energy in SHM

Looks like: K/U exchange, amplitude from E, or mean values

Fast model: E = ½kA² = ½mω²A²; K+U=E at every point.

Physical / torsional / angular SHM

Looks like: Pendulum, rod, or torsional constant κ

Fast model: Small-angle: τ = −κθ ⇒ ω=√(κ/I).

Damped / forced / resonance sketch

Looks like: Qualitative amplitude–frequency or decay

Fast model: Name under/critical/overdamped; resonance near ω₀ for light damping.

Method 01 · Potential superposition

Potential is easier than vector g for assemblies and energy questions.

Do this: Add scalar V from each spherical/point piece; then g=−∇V or use symmetry for g.

Method 02 · Energy to infinity

One criterion covers surface escape, escape from orbit, and ‘minimum energy to remove’.

Do this: Escape and binding questions: require E≥0 at infinity relative to V∞=0.

Method 03 · Kepler ratio cancel GM

Avoids inserting G and M when only ratios are asked.

Do this: For two orbits about same centre, (T₁/T₂)²=(a₁/a₂)³.

Method 04 · Shell theorem gate

Prevents using GM/r² inside cavities or thick shells wrongly.

Do this: Outside: as point mass at centre; inside a thin shell: g=0, V=constant=−GM/R.

Field and potential of spherical mass

Looks like: Point outside/inside uniform sphere or shell

Fast model: Outside: like point mass; inside shell E=0; inside solid E∝r.

Orbital mechanics / Kepler

Looks like: Circular orbit, period, energy, or escape

Fast model: Use GMm/r² = mv²/r and E=−GMm/(2r) for circular.

Satellite transfer and energy change

Looks like: Raise orbit, geostationary, or binding energy

Fast model: ΔE from E=−GMm/(2a) between orbits.

Gravitational self-energy / binding

Looks like: Uniform sphere self-energy or dismantling work

Fast model: U_self = −(3/5)GM²/R for uniform sphere (standard result).