📖 MODULE 1 — CORE CONCEPTS
Newton's Laws of Motion
Built from first principles. Every concept explained with the examiner's lens — not the textbook lens.
Newton's First Law — Law of Inertia
STATEMENT
"Every body continues in its state of rest or of uniform motion in a straight line unless acted upon by a net external force."
What is Inertia?
Inertia is the resistance of a body to change in its state of motion. It is NOT a force. It is a property.
- Inertia of rest → tendency to stay at rest
- Inertia of motion → tendency to stay in motion
- Inertia of direction → tendency to keep moving in same direction
- Measure of inertia = mass (more mass = more inertia)
Students write "inertia is the force that keeps a body at rest." NO. Inertia is NOT a force. You will lose marks for this in CBSE definitional questions.
First Law is actually a special case of Second Law (when F=0, a=0). But it defines what an inertial reference frame is — critical for JEE Advanced.
Types of Inertia — Exam Examples
- A passenger jerks backward when bus suddenly starts — passenger's inertia keeps them at rest
- Dust falls when carpet is beaten — carpet moves, dust stays momentarily
- Tablecloth trick — tablecloth pulled fast, dishes stay due to inertia
- Coin on cardboard — flick cardboard away, coin drops into glass
In JEE, they ask: "Why does the body jerk?" Always identify WHICH type of inertia and from whose frame.
- Passenger jerks forward when bus suddenly stops
- Athlete runs before long jump — uses inertia of motion
- Ball rolling on floor (if no friction) — continues indefinitely
- Mud thrown off spinning wheel — tangential inertia
- Stones fly tangentially when rotating circular platform stops suddenly
- Water in bucket follows circular path until released
- Cyclist leans while turning — direction inertia must be overcome
CBSE exam typically asks one 2-mark question identifying the type of inertia. NEET asks which example is not an example of Newton's First Law. Know all three types cold.
KEY IMPLICATION — FOR JEE
First Law defines an inertial frame. If a frame is non-inertial (accelerating), you must introduce a pseudo force = −ma in that frame. This is tested heavily in JEE Advanced.
Newton's Second Law
STATEMENT
F⃗ = dp⃗/dt = ma⃗
Rate of change of momentum = Net external force
Critical Points:
- F is the NET external force — not just any force
- F and a are always in the same direction
- F = ma is valid only in inertial frames
- m is constant (classical mechanics) → F = m(dv/dt)
- For variable mass: F = v(dm/dt) + m(dv/dt) [Rocket equation]
"This is where most students lose marks." When multiple forces act on a body, students write F₁ = ma instead of (F₁ + F₂ + F₃) = ma. ALWAYS draw FBD first.
Resolution of Forces:
Apply Newton's 2nd Law separately in each direction:
ΣFx = max ΣFy = may
Derivation: F = ma from F = dp/dt
p = mv (momentum)
F = dp/dt = d(mv)/dt
For constant mass m:
F = m(dv/dt) = ma
∴ F = ma ✓
For variable mass (rocket): Fnet = ma + vrel(dm/dt). The thrust force is T = vrel(dm/dt). JEE Advanced tests this.
Common Scenarios:
F - f = ma (where f = friction). Forces along horizontal are equated to ma. Normal force N = mg (no vertical acceleration).
Along plane: mg sinθ - f = ma. Perpendicular to plane: N - mg cosθ = 0. Always resolve along and perpendicular to the incline.
- Moving up with acceleration a: N = m(g + a) → "apparent weight increases"
- Moving down with acceleration a: N = m(g - a) → "apparent weight decreases"
- Free fall (a = g): N = 0 → "weightlessness"
- If string tension T replaces N in hanging body: Same logic applies
JEE twists the elevator concept by adding a spring balance or asking apparent weight vs real weight. The formula changes but the FBD logic stays the same.
Newton's Third Law
STATEMENT
"For every action, there is an equal and opposite reaction. They act on DIFFERENT bodies."
Critical Conditions — Action-Reaction Pair:
- Equal in magnitude
- Opposite in direction
- Same nature (both contact, or both gravitational, etc.)
- Act on DIFFERENT bodies (cannot cancel each other)
- Simultaneous — they appear and disappear together
"Action and reaction cancel each other." This is the #1 misconception. They act on DIFFERENT bodies — they can never cancel. If you write this in exam, expect zero marks.
Real Examples:
- Book on table: Book pulls Earth up (gravity), Earth pulls book down → action-reaction between book and Earth
- Gun-bullet: Bullet forward, gun recoils backward
- Rocket: Gas expelled backward, rocket thrust forward
- Swimming: Push water backward, water pushes swimmer forward
- Walking: Foot pushes Earth backward, Earth pushes foot forward
NEET frequently asks: "Identify the reaction to gravitational force of Earth on Moon." Answer: Gravitational force of Moon on Earth. Same nature, different bodies.
Horse-Cart Paradox — JEE Favourite
Question: If horse pulls cart with force F, cart pulls horse back with F (3rd Law). Then why does the cart-horse system move?
Answer: The two equal-opposite forces act on DIFFERENT bodies (horse and cart), so they don't cancel. The system moves because:
- Friction from ground on horse's feet pushes horse forward
- Net force on horse = Ground friction - Tension from cart > 0
- Net force on cart = Tension from horse - Friction on cart > 0
Third Law in Multi-Body Problems:
When two blocks A and B are in contact and force F is applied on A:
Contact force N between A and B:
A pushes B with force N → B pushes A with force N (3rd Law)
For system: F = (m_A + m_B) × a → a = F/(m_A + m_B)
For block B alone: N = m_B × a = m_B × F/(m_A + m_B)
Contact force N between A and B:
A pushes B with force N → B pushes A with force N (3rd Law)
For system: F = (m_A + m_B) × a → a = F/(m_A + m_B)
For block B alone: N = m_B × a = m_B × F/(m_A + m_B)
When solving multi-body problems, always apply 3rd Law to find contact forces. Never forget the reaction force when analyzing individual bodies.
Momentum & Impulse
DEFINITIONS
p⃗ = mv⃗ [kgm/s or Ns]
J⃗ = F⃗·Δt = Δp⃗ [Ns]
J⃗ = ∫F dt (for variable force)
Conservation of Momentum:
CONSERVATION LAW
m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'
Valid when net external force = 0
- Momentum is a vector — direction matters
- Conserved in all directions independently
- Total momentum of isolated system = constant
- Internal forces cannot change total momentum
Students forget that momentum conservation works component-wise. If explosion happens at 45°, conserve px and py SEPARATELY.
Impulse — Key Concepts:
- Impulse = Area under F-t graph
- For constant force: J = F × Δt
- For variable force: J = ∫F dt
- Impulse = Change in momentum (always)
- Favg = J / Δt → used in collision problems
Impulse-Momentum Theorem: Impulse = Δp. This is just Newton's 2nd Law integrated over time. JEE Advanced uses this to find average force during brief collisions (cricket ball hit, car crash, etc.)
Applications in Exam:
Initial momentum = 0. After firing: m_bullet × v_bullet + m_gun × v_gun = 0. So v_gun = -m_bullet × v_bullet / m_gun. Gun recoils in opposite direction.
Object at rest explodes into pieces. Total momentum = 0. Each piece's momentum is equal and opposite to sum of others. JEE asks about KE gained — comes from chemical energy.
F_thrust = v_rel × (dm/dt). As mass decreases, if thrust is constant, acceleration increases. This is variable mass — Newton's 2nd Law modified form.
Momentum conservation + impulse is tested in 2-3 NEET questions per year. Always check: "Is the system isolated?" If yes, conserve momentum. If not, use impulse-momentum theorem.
Laws of Friction
THREE TYPES OF FRICTION
Static Friction (fs)
fs ≤ μsN | Adjustable — matches applied force until max
Kinetic Friction (fk)
fk = μkN | Constant while sliding | μk < μs always
Rolling Friction (fr)
fr = μrN | Smallest | μr < μk < μs
Laws of Friction (Empirical):
- Friction is proportional to normal force: f = μN
- Friction is independent of area of contact
- Kinetic friction is independent of speed
- Friction depends on nature of surfaces (μ)
"More area = more friction." WRONG. Friction is independent of contact area (empirical law). This is tested directly in NEET and CBSE theory questions.
Angle of Friction & Angle of Repose:
tan λ = μs (angle of friction λ)
θ_repose = λ (angle of repose = angle of friction)
tan θ_repose = μs
Angle of repose = Angle at which body just starts to slide on incline. At this angle: mg sinθ = μs × mg cosθ → tan θ = μs. JEE often asks: "Find minimum force to move body on rough incline" — this uses angle of friction concept.
f vs Applied Force Graph:
Friction Force vs Applied Force
fs(max) = μsN
fk = μkN
Body starts sliding
Static friction rises with applied force, then drops to kinetic value when body slides
This graph is asked in CBSE 3-5 mark questions and JEE as an "identify the graph" question. Know that static peak > kinetic plateau.
Circular Motion & Newton's Laws
Circular motion requires a centripetal force directed toward the center. This force is provided by different sources depending on the scenario.
CENTRIPETAL FORCE
F_c = mv²/r = mω²r = mω²r
Always directed toward center. NOT a separate force.
Centripetal force is NOT a separate force. It is the net component of all forces toward the center. Writing "centripetal force" on FBD as a separate force will cost marks in JEE.
Source of Centripetal Force in Each Case:
| Scenario | Source of F_c |
|---|---|
| Stone on string (horizontal) | Tension T |
| Car on circular road (flat) | Friction |
| Car on banked road | N sinθ + f cosθ |
| Planet orbiting Sun | Gravitational force |
| Electron in atom (Bohr) | Electrostatic force |
| Vertical circular motion (top) | T + mg (both toward center) |
Banking of Roads:
For ideal banking (no friction):
tan θ = v²/rg
For max speed with friction:
v_max = √[rg(tan θ + μ)/(1 - μ tan θ)]
For min speed with friction:
v_min = √[rg(tan θ - μ)/(1 + μ tan θ)]
Vertical Circular Motion:
- At bottom: T - mg = mv²/r → T = m(g + v²/r)
- At top: T + mg = mv²/r → T = m(v²/r - g)
- Minimum speed at top: v_min = √(gr) (when T = 0)
- Minimum speed at bottom: v_min = √(5gr)
- T_bottom - T_top = 6mg (always, irrespective of position)
The condition T_bottom - T_top = 6mg is a JEE favourite shortcut. Derive it once: it comes from energy conservation between top and bottom combined with circular motion equation.
For NEET: Focus on flat road and banking formulas. For JEE Main: Add vertical circular motion. For JEE Advanced: Variable speed circular motion with energy conservation.
Concepts Clear? Now Learn the Formulas.
Every formula with derivation, dimensional analysis, and search tool.