Laws of Motion — CBSE · NEET · JEE Master Guide

CBSE Class 11 · NEET · JEE Master Guide

Laws of Motion

Visual · Intuitive · Exam-Oriented. Everything a NEET/JEE aspirant needs — from zero to mastery in one guide.

⚡ Newton's 3 Laws 🔥 High NEET Weightage 📐 FBD Mastery 🧮 45+ Practice Questions

Newton's Laws

Key Formulas

45+

Practice Questions

Common Mistakes

NCERT Chapter Map & Exam Blueprint

Force & Inertia🔥 Very High⚠️ Confusing

Newton's First Law🌟 Medium⚠️ Tricky MCQs

Newton's Second Law (F=ma)🔥 Very High🎯 Numericals

Newton's Third Law🌟 Medium⚠️ Most Confused

Momentum & Impulse🔥 Very High🎯 NEET Fav

Free Body Diagrams (FBD)🔥 Very High⚠️ Often Skipped

Friction (Static + Kinetic)🔥 Very High⚠️ Direction Trap

Inclined Plane + Elevator🔥 Very High🎯 Special Cases

CBSE Board

2–3 questions · 5–10 marks total
Expect: Numericals + Conceptual
FBD drawing is mandatory for full marks

NEET Exam

3–4 MCQs typically per year
FBD + Friction dominate
Incline + Connected body combos are frequent

What is Force?

A force is simply a push or pull. When you push a door, kick a football, or pull a drawer — you're applying a force. Forces are vectors: they have both magnitude (how much?) and direction (which way?).

Unit: Newton (N) | Dimension: [MLT⁻²]

What is Inertia? (Objects are Lazy!)

Inertia is the tendency of an object to resist any change in its state. Objects are naturally "lazy" — they don't want to start moving if at rest, and if moving, they don't want to stop!

Key Insight: Mass = Measure of Inertia

A truck is harder to stop than a bicycle — because it has more mass = more inertia.

REAL LIFE EXAMPLES

🚌

Bus Stops SuddenlyYou lean forward — your body was moving and by inertia wants to keep going!

🏃

Bus Starts SuddenlyYou lean backward — your body was at rest and resists the new motion by inertia.

🎩

Tablecloth TrickPull fast — dishes stay! Their inertia of rest resists the sudden movement.

⚽

Rolling FootballOn a smooth surface it would roll forever — inertia of motion keeps it going!

MOMENTUM & IMPULSE

Momentum (p = mv)

p = mv

Why does a cricket ball hurt more than a tennis ball at the same speed? Cricket ball has more mass → more momentum → more impact!

Conservation of Momentum:If no external force acts, total momentum before = total momentum after. A gun recoils when a bullet fires — conservation in action!

Impulse (J = F × t)

J = F·Δt = Δp

Why do boxers wear gloves? Gloves increase time of impact → same impulse spread over more time → less peak force. Same logic: bending knees on landing, pulling hands back when catching a ball!

🥇 First Law — Law of Inertia

"Every object continues in its state of rest or uniform motion unless an external force acts on it."

Net F = 0 ⟹ a = 0

Simple meaning: Things don't change what they're doing unless pushed or pulled. An object at rest stays at rest. An object moving keeps moving at the same speed in the same direction.

When to use: When a body is in equilibrium (stationary or constant velocity). Net force = 0 means all forces balance.

🚀 Astronaut floating in space — no friction, no air resistance — continues drifting forever with no force needed!

🥈 Second Law — F = ma

"The rate of change of momentum is proportional to the applied force and occurs in the direction of force."

F = ma = Δp/Δt

Simple meaning: Bigger net force = bigger acceleration. More mass = less acceleration for the same force. The F here is always the NET force — sum of ALL forces!

F increases →Acceleration increases (same mass)

Mass increases →Acceleration decreases (same F)

🏎️ F1 car: massive engine force + ultra-light body = extraordinary acceleration. F=ma working perfectly!

🥉 Third Law — Action-Reaction

"For every action, there is an equal and opposite reaction."

F_AB = −F_BA

CRITICAL POINT: Action and reaction act on DIFFERENT objects — they NEVER cancel each other!

Common confusion: "If forces are equal and opposite, why does anything move?" → Because they act on different bodies! Force on you ≠ force on wall. They can't cancel — you'd need to subtract forces on the same object to cancel!

🚀 Rocket: gases push down (action) → rocket goes up (reaction). 🚶 You walk: foot pushes Earth back → Earth pushes you forward!

Newton's Laws — Common Mistakes

❌

Action-Reaction Cancel Out

Students think action and reaction forces cancel because they're equal and opposite.

✅ They act on DIFFERENT objects — cancellation only happens when two forces act on the SAME object.

❌

Moving = Net Force Exists

Assuming that if an object moves, there must be a net force acting on it.

✅ Object can move at constant velocity with ZERO net force (Newton's 1st Law!)

❌

F includes all forces, even balanced

Using total force including forces that cancel in F = ma.

✅ Always use NET force (ΣF). 10N right + 3N left = 7N net to the right.

Free Body Diagram — Step by Step Method

FBD is your most powerful tool in mechanics. Draw it for EVERY problem before writing a single equation!

Isolate the object — Draw just the object alone (a box, circle). Remove everything else from the picture.

Identify ALL forces — Weight (always ↓), Normal force, Tension, Applied force, Friction. Miss none!

Draw arrows from centre — Each force gets an arrow pointing in the direction the force acts. Length = magnitude.

Label every arrow — F, N, mg, T, f — never leave arrows unnamed. Examiners check this!

Apply Newton's 2nd Law — ΣFₓ = maₓ and ΣFᵧ = maᵧ for each direction separately.

// FBD 01 — Block at Rest on Table

// FBD 02 — Block Being Pushed (with friction)

Golden Rules for FBD

Rule 1 — Weight always pulls DOWNWeight = mg, always toward Earth's centre. NEVER forget this force in your FBD!

Rule 2 — Normal force ⊥ to surfaceOn a flat table: N points up. On an incline: N is perpendicular to the incline surface (NOT vertical)!

Rule 3 — Friction opposes relative motionObject moves right → friction points left. Object tends to move right → friction still points left.

Rule 4 — Tension pulls, never pushesStrings and ropes only pull. Tension always acts away from the object along the string direction.

Friction — The Resistance Force

Friction is the force that opposes relative motion (or tendency of motion) between surfaces in contact. Without friction, you couldn't walk, write, or drive!

STATIC FRICTION

f_s ≤ μ_s N

Object is NOT moving yet. Friction adjusts to match applied force up to a maximum limit.

Example: Pushing a heavy box that doesn't budge yet

LIMITING FRICTION

f_l = μ_s N

Maximum static friction — the tipping point just before sliding begins.

Example: Moment just before box starts sliding

KINETIC FRICTION

f_k = μ_k N

Object IS moving. Always constant. Always less than limiting friction.

Example: Box sliding across the floor

// Friction vs Applied Force Graph (must know!)

SPECIAL CASES

📐 Inclined Plane (angle θ)

Forces on a block on incline:

N = mg cosθ (perpendicular) mg sinθ — along incline (down) f = μN = μmg cosθ (friction)

⭐ Angle of repose: tan θ = μ (just about to slide)

🏗️ Block Slides If…

Condition for sliding down:

mg sinθ > μ mg cosθ ⟹ tan θ > μ

Common mistake: Using N = mg on incline. Always use N = mg cosθ!

🛗 Elevator Problems

Accelerating UP ↑

N = m(g+a)

"You feel heavier"
Apparent weight > Real weight

Constant Speed or REST

N = mg

"You feel normal"
Apparent = Real weight

Accelerating DOWN ↓

N = m(g−a)

"You feel lighter"
Apparent weight < Real weight

Free Fall (a = g):N = m(g−g) = 0 → Weightlessness! This is exactly what astronauts experience in orbit.

Complete Formula Sheet — Exam Weapon

Newton's 2nd Law

F = ma

Net force and acceleration problems. Always use NET force!

Momentum

p = mv

Conservation problems, collisions, impulse calculations

Impulse

J = FΔt = Δp

Variable force, time of contact, sudden impacts

Kinetic Friction

f_k = μ_k N

When object IS already sliding on the surface

Static Friction (max)

f_s = μ_s N

Just before object starts moving (limiting case)

Normal on Incline

N = mgcosθ

Block on inclined plane — ALWAYS use this, not mg!

Elevator (up accel)

N = m(g+a)

Upward acceleration OR decelerating while going down

Elevator (down accel)

N = m(g−a)

Downward acceleration OR decelerating while going up

Atwood Machine

a = (m₂−m₁)g / (m₁+m₂)

Two masses over a frictionless pulley

Tension (Atwood)

T = 2m₁m₂g / (m₁+m₂)

String tension in Atwood machine setup

Memory Tricks — Never Forget

FOR F = ma

"FMA" like a wrestling finishing move — Force Makes Acceleration! The bigger the Force, the more the Acceleration.

ELEVATOR N = m(g±a)

Going UP? Add acceleration (+a). Going DOWN? Subtract (−a). When you ride an elevator up, you feel heavier — so add!

INCLINED PLANE COMPONENTS

Along the incline → sin θ. Away from incline (normal) → cos θ. "Sin goes along the slope, Cos stays perpendicular."

STATIC vs KINETIC FRICTION

Static is Stronger (μ_s > μ_k). Kinetic is Kinder (lower value). Easier to keep sliding than to start sliding!

5-Step Problem Solving Strategy

READ carefully — Identify: what's given (F, m, a, μ, θ, v) and what's asked. Write it down!

DRAW FBD — Isolate object, draw ALL forces with arrows and labels. NEVER skip this step!

CHOOSE axes — One along motion, one perpendicular. On incline: along incline & perpendicular to it.

WRITE equations — ΣFₓ = maₓ and ΣFᵧ = maᵧ. Fix + and − directions and be consistent throughout!

SOLVE & CHECK — Verify units, check if answer makes physical sense (negative mass = impossible!)

NEET Shortcuts

Two blocks on smooth surface:For total acceleration: a = F/(m₁+m₂). For tension between blocks: T = m₂ × a. Use system approach first, then individual block for T.

Atwood machine:Acceleration a = (m₂−m₁)g/(m₁+m₂). Tension T = 2m₁m₂g/(m₁+m₂). These are NCERT standard — memorise both!

Incline + block + pulley combo:Treat as a system first → find acceleration. Then use individual body FBD to find tension. This is NEET's favourite question type!

⚠️ Exam Traps to Avoid

Trap 1 — Normal Force on Incline:On an inclined plane, N = mg cosθ — NOT mg. Hundreds of students lose marks here every year. Always decompose!

Trap 2 — Sign Convention:Decide your positive direction BEFORE solving. If you choose right as positive, stick to it. One sign error flips your entire answer!

Trap 3 — Net Force vs Total Force:F = ma uses NET force only. Subtract opposing forces. Don't use the magnitude of individual forces directly.

Trap 4 — Mass vs Weight:60 kg is mass. Weight = 60 × 10 = 600 N. NEET MCQs often give mass and expect you to use weight — watch for this!

Top 8 Mistakes Students Make

❌

Missing Normal Force in FBD

Forgetting the normal force, especially when the object is on an inclined surface.

✅ Every surface in contact generates a normal force perpendicular to it. No exceptions!

❌

N = mg on an Inclined Plane

Using mg as normal force on incline — one of the most common and costly mistakes in exams.

✅ On an incline: N = mg cosθ. Normal means perpendicular to the surface!

❌

Action-Reaction on the Same Object

Trying to "cancel" action-reaction pair forces by treating them as acting on the same body.

✅ Action-reaction ALWAYS acts on DIFFERENT objects. They can never cancel each other.

❌

Wrong Direction of Friction

Drawing friction in the wrong direction — along motion or away from motion instead of opposing it.

✅ Friction opposes relative motion (or tendency). Block moves right → friction is left.

❌

Not Using Net Force in F = ma

Including all forces without proper signs, or using total magnitude instead of net force.

✅ F_net = ΣF (with signs). 10N right − 3N friction = 7N net. Then F_net = ma.

❌

Confusing Mass and Weight

Using 60 kg as weight in force equations instead of converting to Newtons.

✅ Weight = mg. 60 kg × 10 m/s² = 600 N. Always convert mass to weight first!

❌

Wrong Momentum Units

Writing momentum in Newtons (N) instead of the correct unit kg·m/s.

✅ p = mv → units = kg × m/s = kg·m/s. NOT Newtons! (Newtons = kg·m/s²)

❌

Ignoring Changed N in Elevator + Friction

In elevator problems with a sliding object, forgetting that friction changes because N changes.

✅ In elevator: N changes → friction f = μN also changes! Recalculate friction with new N.

One-Page Quick Revision

NEWTON'S LAWS

1st Law: No net F → No acceleration
2nd Law: F = ma (net force!)
3rd Law: Equal & opposite, different bodies

KEY FORMULAS

p = mv (momentum)
J = FΔt = Δp (impulse)
f = μN (friction)
N = mgcosθ (incline)

FRICTION FACTS

μ_s > μ_k (static > kinetic)
Friction opposes relative motion
Angle of repose: tanθ = μ
f_s ≤ μ_s N (not always equal!)

ELEVATOR QUICK CHECK

Accelerate up: N = m(g+a)
Accelerate down: N = m(g−a)
Constant/rest: N = mg
Free fall: N = 0

FBD CHECKLIST

Weight (mg) ↓ always present
Normal ⊥ to surface
Tension pulls, never pushes
Friction opposes motion

CONSERVATION CHECK

p conserved if F_ext = 0
Impulse = change in momentum
Collision: p_before = p_after
Gun recoil is conservation!

Exam Strategy

CBSE BOARD TIPS

Always show FBD explicitly in answers — teachers give step marks even if final answer is wrong. For 5-mark questions: FBD (1) + setting up equations (2) + calculation (1) + answer with correct unit (1). Write direction clearly for vector answers.

NEET MCQ TIPS

For tricky options: eliminate wrong units first. If two options look right, check friction direction. Inclined plane + friction + connected body is NEET's all-time favourite combo question. Expect 1–2 such combos each year!

AVOIDING NEGATIVE MARKS

If unsure: check if all forces appear in your FBD. Verify sign convention. Eliminate options with wrong units first — that alone narrows to 2 options. Never guess randomly; use elimination and attempt only when ≥ 2 options eliminated.