JEE/NEET Physics · Laws of Motion series · Part 8 of 8 · All parts →
- Eight parts on one card — the most-used formulas in JEE/NEET mechanics
- F_net = ma · N = m(g ± a) · Atwood a = (m₂−m₁)g/(m₁+m₂)
- friction: f ≤ μ_s N, f = μ_k N · repose tan⁻¹μ_s
- banking tanθ = v²/rg · vertical circle √(gr) top, √(5gr) bottom
- impulse J = FΔt = Δp · momentum conserved without external force
The final card of the Laws of Motion series — eight parts on one revision sheet, plus the machines, vehicles and safety systems built on these three laws.
- The master formula card
- The one-rule-per-part recap
- Newton’s laws in the wide world
- Final practice set
- Recap
The Master Formula Card
| What | Formula / rule | Remember |
|---|---|---|
| Second law | F_net = ma | net force only, per axis |
| Elevator | N = m(g ± a) | heavier up, lighter down |
| Weightlessness | a = g → N = 0 | gravity still on |
| Atwood machine | a = (m₂−m₁)g/(m₁+m₂) | difference pushes total |
| Incline | a = g sinθ · N = mg cosθ | sin slides, cos clings |
| Static friction | f ≤ μ_s N | adjusts as needed |
| Kinetic friction | f = μ_k N | fixed, smaller than static |
| Angle of repose | tanθ = μ_s | slide-point of inclines |
| Flat-bend max speed | v = √(μrg) | friction supplies mv²/r |
| Banking (optimum) | tanθ = v²/rg | no friction needed |
| Vertical circle top | v_min = √(gr) | N = 0 critical |
| Vertical circle bottom | N = mv²/r + mg | heaviest point |
| Full-circle release | v_bottom = √(5gr) | energy + critical top |
| Impulse | J = FΔt = Δp | area under F-t |
| Momentum conservation | Σp constant (no external F) | crashes, recoil, rockets |
The One-Rule-Per-Part Recap
1: laziness, recipe, pairs — and always draw the FBD. 2: felt weight is the normal force. 3: connected masses share tension’s discipline. 4: static adjusts, kinetic is fixed. 5: tilt the push, steer the car. 6: gravity helps at the top, bites at the bottom. 7: stretch the time, shrink the force.
Newton’s Laws in the Wide World
- Every bridge and building is F_net = 0 writ large: structural engineering is organized non-acceleration, with tension and compression members playing the force roles.
- Car safety evolved through this chapter — crumple zones (cushion principle), ABS (static friction), seatbelts (first law): three laws, three saved lives per feature.
- ISRO launches — rockets are third-law machines climbing on momentum conservation, with every stage separation an impulse bookkeeping exercise.
- Artificial joints and biomechanics — hip implants are sized by the m(g+a) of stairs and steps: doctors doing elevator physics with bone.
- Sports science — from boxers riding punches (Δt stretching) to skaters spinning (momentum), athletic coaching is applied Newton.
Aristotle’s physics needed a god for every motion; Newton’s needs only three sentences and bookkeeping. That’s the revolution: the same rules for apples, moons, muscles and machines — one grammar for everything that pushes or is pushed. Modern engineering is these laws with budgets attached.
One bridge span: every member’s tension computed from F = 0 at every joint — millions of Newton equations solved before a single bolt. One rocket launch: thrust by third law, ascent by F = ma with shrinking mass, orbit by circular chapters — the whole syllabus flying together.
Picture the whole series as one FBD album: a lifter (N = m(g+a)), an Atwood pair, a slope slider, a braking car, a banked curve, a loop rider, a catching cricketer — seven scenes, one dot-with-arrows method. Flip through the album and you flip through 300 years of applied physics.
Practice set (answers hidden — try first)
(NEET-level) 5 kg at 2 m/s² needs net force:
(JEE Main-level) Lift down at 2 (g=10), 50 kg: N =
(NEET-level) μ_s = 0.75, N = 200 N: max static friction =
(JEE Main-level) r = 25 m, v = 15 (g=10): bank tanθ =
(NEET-level) 0.2 kg at 10 m/s caught in 0.05 s: F =
- F = ma per axis, FBD always
- elevator and apparent weight
- inclines, pulleys, friction laws
- banking and vertical circles
- impulse-momentum and conservation
- 🔁 the 15-row master card
- 🔁 one rule per part
- 🔁 Newton’s laws = the grammar of engineering
- 🧠 Full-card chant: ‘diagram it, resolve it, adjust it, tilt it, time it’.
- 🏠 Daily: bridges = organized F = 0.
- 🏠 Daily: crumple zones are cushion principle.
Quick revision
- Eight parts on one card — the most-used formulas in JEE/NEET mechanics
- F_net = ma · N = m(g ± a) · Atwood a = (m₂−m₁)g/(m₁+m₂)
- friction: f ≤ μ_s N, f = μ_k N · repose tan⁻¹μ_s
- banking tanθ = v²/rg · vertical circle √(gr) top, √(5gr) bottom
- impulse J = FΔt = Δp · momentum conserved without external force
- The one-rule-per-part recap
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