Mechanics is the study of how things move and why. From Newton's laws to simple machines — these concepts appear in CDS, NDA & AFCAT every single year, and are completely learnable even from scratch.
Beginner FriendlyCDS · NDA · AFCAT25 Practice Questions
This module covers: distance vs displacement, speed vs velocity, Newton's three laws, gravitation, friction, work, energy and power, and simple machines. No complex math — just the concepts, formulas in plain English, and the exact patterns that appear in CDS/NDA/AFCAT.
Scalar vs vector — the first distinction in mechanics
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When an object moves, we can describe its change in position in two ways — distance (how much total path it covered) and displacement (how far it is from where it started, in a straight line).
Feature
Distance
Displacement
Definition
Total path length covered
Shortest straight-line distance from start to end point
Type
Scalar (magnitude only)
Vector (magnitude + direction)
Can be zero?
Only if object doesn't move
Can be zero even if object moves (e.g. full circle)
Can be negative?
Never
Yes (depends on direction)
Example
Running 400m on a track
Back at start = 0 displacement
Simple Analogy
Imagine walking from your room to the kitchen and back. Distance = total steps walked. Displacement = zero (you ended where you started).
⚑ Exam Trap
If a person runs one complete lap of a circular track of radius r, distance = 2πr but displacement = zero. This exact scenario appears in CDS/NDA multiple times.
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Speed, Velocity & Acceleration
How fast, how fast in which direction, and how fast is it changing
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Quantity
Definition
Type
Formula
Speed
Distance covered per unit time
Scalar
Speed = Distance ÷ Time
Velocity
Displacement per unit time
Vector
Velocity = Displacement ÷ Time
Acceleration
Rate of change of velocity
Vector
a = (v − u) ÷ t
Equations of Motion (3 Golden Equations)
v = u + at → Final velocity = Initial velocity + (acceleration × time)
s = ut + ½at² → Distance = (initial vel × time) + ½(accel × time²)
An object continues to be in its state of rest or uniform motion in a straight line unless acted upon by an external unbalanced force.
Inertia is the tendency of an object to resist change in its state of motion. More mass = more inertia.
Real-Life Examples
When a bus suddenly brakes, passengers lean forward (their body resists the change — inertia of motion)
When a bus suddenly starts moving, passengers lean backward (inertia of rest)
A ball rolling on a smooth surface keeps rolling — no friction means nothing stops it
Shaking a wet umbrella — water flies off (inertia of motion of water droplets)
⚑ Exam Trap
The First Law is also called the "Law of Inertia". Inertia depends on mass only — NOT on velocity, shape, or size. A heavier truck has more inertia than a bicycle.
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Second Law — Law of Force & Acceleration
F = ma — the most used formula in mechanics
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Newton's Second Law
The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction of the force.
F = ma → Force = Mass × Acceleration
Key Formulas from Second Law
F = ma → Force (N) = mass (kg) × acceleration (m/s²)
Momentum (p) = mv → mass × velocity. SI unit = kg·m/s
F = Δp ÷ t → Force = change in momentum ÷ time
Impulse = F × t = Δp → Force × time = change in momentum
Key Points
SI unit of Force = Newton (N) = kg·m/s²
SI unit of Momentum = kg·m/s
Impulse explains why: catching a ball slowly hurts less (longer time = smaller force)
A fielder draws their hands back while catching a ball — to increase time and reduce force (impulse)
Seat belts, airbags, and padding all work on the impulse principle
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Third Law — Law of Action & Reaction
"Every action has an equal and opposite reaction"
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Newton's Third Law
For every action, there is an equal and opposite reaction. The two forces always act on different objects — never on the same object.
The Third Law leads to the Law of Conservation of Momentum: in the absence of external forces, the total momentum of a system remains constant. Gun + bullet example: momentum before firing = 0. After firing: bullet forward momentum = gun backward momentum (recoil). This is directly tested.
Section 3 — Gravitation
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Newton's Law of Gravitation & 'g'
Why things fall and how fast they fall
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Universal Law of Gravitation
Every two objects in the universe attract each other with a force that is:
— directly proportional to the product of their masses
— inversely proportional to the square of the distance between them
Gravitation Formulas
F = Gm₁m₂ / r² → G = 6.67 × 10⁻¹¹ N·m²/kg² (Universal constant)
g = GM/R² → g on Earth surface ≈ 9.8 m/s² (use 10 m/s² in exams)
Weight = mg → Weight (N) = mass (kg) × g (m/s²)
Key Facts on 'g' — Very Frequently Asked
g decreases as you go higher above Earth's surface
g decreases as you go deeper inside the Earth
g is maximum at the poles (Earth is flatter, closer to centre)
g is minimum at the equator
g on Moon = g/6 = about 1.63 m/s² (1/6th of Earth's)
Mass = constant everywhere · Weight = varies with location
In free fall / space — weightlessness (weight = 0, mass ≠ 0)
⚑ Most Tested Trap — Mass vs Weight
Mass = amount of matter. Measured in kg. Does NOT change anywhere in universe.
Weight = gravitational force on the mass = mg. Changes with location (moon, poles, equator).
An astronaut in space has mass but is weightless (apparent weight = 0).
Section 4 — Friction
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Friction — The Necessary Evil
Types, causes, and how to increase or reduce it
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Friction is a force that opposes the relative motion between two surfaces in contact. It acts parallel to the surface and opposite to the direction of motion.
Type
Description
Example
Static friction
Acts when object is at rest — prevents start of motion. Highest friction.
Pushing a heavy box that won't move
Sliding/Kinetic friction
Acts when object is moving. Less than static.
Block sliding on a table
Rolling friction
Acts when object rolls. Least of all three.
Ball rolling on ground
Fluid friction
Resistance in liquids/gases. Also called drag/viscosity.
Fish swimming in water
Order of Friction (Highest → Lowest)
Static > Sliding (Kinetic) > Rolling
This is why wheels were invented — rolling friction is far less than sliding
Friction increases with: rough surfaces, more weight (normal force)
Useful friction: walking, writing, brakes, matches, climbing Harmful friction: wear and tear of machines, heat generated in engines, tyre wear
Section 5 — Work, Energy & Power
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Work & Energy
Definitions, formulas and conservation law
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Definition of Work (in Physics)
Work is done when a force causes displacement in the direction of the force. W = F × d × cos θ (θ = angle between force and displacement)
Work, Energy & Power Formulas
Work (W) = F × d → Unit = Joule (J). 1 J = 1 N × 1 m
KE = ½mv² → Kinetic energy = ½ × mass × velocity²
PE = mgh → Potential energy = mass × g × height
Power (P) = W ÷ t → Unit = Watt (W). 1 Watt = 1 J/s
1 Horsepower = 746 Watts
1 kWh = 3.6 × 10⁶ J → unit of electrical energy (unit of electricity)
Law of Conservation of Energy
Energy can neither be created nor destroyed — only converted from one form to another
Total KE + PE = constant (in absence of friction) — called mechanical energy
At the highest point of a pendulum: PE is maximum, KE is zero
At the lowest point of a pendulum: KE is maximum, PE is zero
A falling object: PE converts to KE as it falls
⚑ When is Work ZERO?
Force is applied but no displacement (pushing a wall — no work done)
Force is perpendicular to displacement (cos 90° = 0): a coolie carrying luggage on his head while walking horizontally — force is upward, displacement is horizontal — work done by coolie = 0
This "coolie" example is a classic CDS/NDA question
Simple machines help us do work more easily — they don't reduce the total work done, but they allow us to apply a smaller force over a larger distance.
Mechanical Advantage (MA)
MA = Load ÷ Effort → Ratio of output force to input force
Efficiency = (Output work ÷ Input work) × 100%
No machine is 100% efficient (friction always causes some energy loss)
Machine
Class / Type
Example
MA
Lever — Class 1
Fulcrum between load and effort
See-saw, scissors, pliers, crowbar
Can be > or < 1
Lever — Class 2
Load between fulcrum and effort
Wheelbarrow, nutcracker, bottle opener
Always > 1
Lever — Class 3
Effort between fulcrum and load
Tweezers, broom, forceps, human forearm
Always < 1
Pulley (fixed)
Changes direction of force
Drawing water from well
= 1
Pulley (movable)
Reduces effort needed
Cranes, elevators
> 1
Inclined plane
Spreads work over longer distance
Ramp, screw, wedge
> 1
⚑ Exam Trap — Human Body as a Machine
Forearm = Class 3 lever (bicep effort is between elbow fulcrum and hand load)
Head nodding = Class 1 lever (neck vertebra is fulcrum)
Standing on tiptoe = Class 2 lever (ball of foot is fulcrum, body weight is load, calf muscle is effort)
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Pressure — Pascal's Law & Archimedes' Principle
Fluids, buoyancy and why ships float
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Pressure Formulas
Pressure = Force ÷ Area → Unit = Pascal (Pa) = N/m²
Fluid pressure = ρgh → density × g × height of fluid column
Pascal's Law
Pressure applied to an enclosed liquid is transmitted equally in all directions. This is the principle behind hydraulic machines — hydraulic brakes, hydraulic lift, hydraulic jack.
Archimedes' Principle
When a body is wholly or partially immersed in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced.
Key Applications — Frequently Asked
A ship floats because it displaces water equal to its own weight
Iron is denser than water, but an iron ship floats because of its hollow shape (displaces more water)
Hydrometer — measures density/specific gravity of liquids using Archimedes' principle
Lactometer — checks purity of milk
Dead Sea — very high salt content → high density → people float easily
A body sinks if its density > liquid; floats if density ≤ liquid
⚑ Pressure Traps
Sharp knife cuts easily — same force, smaller area = more pressure
Snowshoes spread weight over large area = less pressure (don't sink in snow)
High heels = small area = very high pressure on floor
Atmospheric pressure at sea level = 1 atm = 101325 Pa ≈ 1.013 × 10⁵ Pa
Section 7 — Projectile & Circular Motion
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Projectile Motion & Circular Motion
Combined motion concepts for NDA level
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Projectile Motion — Key Facts
Projectile = object thrown at an angle, moves under gravity only
Horizontal velocity remains constant (no air resistance assumed)
Vertical velocity changes due to gravity (g)
Maximum range achieved at angle of 45°
At the highest point: vertical velocity = 0, horizontal velocity = unchanged
Path is always a parabola
Circular Motion — Key Facts
Object moving in circle has centripetal acceleration — directed toward centre
Centripetal force = mv²/r (always directed inward toward centre)
Centrifugal force = apparent outward force felt by the moving object (not a real force — it's a pseudo/fictitious force)
A satellite in orbit is in continuous free fall — centripetal force = gravitational force
Banking of roads — allows vehicles to take turns safely without skidding
⚑ Key Trap — Centripetal vs Centrifugal
Centripetal is a real force directed inward (gravity for satellites, tension for a stone in a sling, friction for a car on a curve). Centrifugal is NOT a real force — it is a feeling of being pushed outward due to inertia. This distinction is directly tested in NDA.
All key formulas, laws and facts from this module — scan this before your exam.
Distance vs Displacement
Distance = total path covered (scalar)
Displacement = shortest straight line, start to end (vector)
One full circle → distance = 2πr · displacement = zero
Speed = Distance ÷ Time (scalar)
Velocity = Displacement ÷ Time (vector)
Acceleration = Change in velocity ÷ Time
Equations of Motion
v = u + at
s = ut + ½at²
v² = u² + 2as
u = initial velocity · v = final velocity
a = acceleration · s = distance · t = time
For free fall: a = g = 9.8 m/s² (use 10)
Newton's Three Laws
1st Law = Law of Inertia · F = 0 → no change in motion
Inertia ∝ mass only
2nd Law: F = ma · Momentum = mv
SI unit of force = Newton (N)
3rd Law: Action = equal and opposite Reaction
Rocket, recoil of gun, swimming = 3rd law
Gravitation
F = Gm₁m₂/r² · G = 6.67×10⁻¹¹ N·m²/kg²
g on Earth ≈ 9.8 m/s² (use 10 in exam)
g on Moon = g/6
g max at poles · g min at equator
g decreases going up OR going deep inside Earth
Mass = constant · Weight = mg (varies)
Friction
Static > Sliding > Rolling (order)
Rolling friction is least → wheels invented
Friction increases: rough surface, more weight
Friction decreases: lubricants, ball bearings
Useful: walking, brakes, writing, matches
Harmful: wear & tear, heat in machines
Work, Energy & Power
W = F×d · Unit = Joule (J)
Work = zero when F ⊥ displacement (coolie example)
KE = ½mv² · PE = mgh
Power = W÷t · Unit = Watt (W)
1 HP = 746 W · 1 kWh = 3.6×10⁶ J
Pendulum bottom: KE max · Top: PE max
Levers & Machines
Class 1: Fulcrum between load & effort → see-saw, scissors
Class 2: Load in middle → wheelbarrow, nutcracker
Class 3: Effort in middle → tweezers, forearm
MA = Load ÷ Effort
No machine = 100% efficient (friction)
Hydraulic machines work on Pascal's Law
Pressure & Buoyancy
Pressure = Force ÷ Area · Unit = Pascal (Pa)
Pascal's Law → hydraulic brakes, lift, jack
Archimedes: buoyant force = weight of fluid displaced
Object floats if density ≤ liquid density
Dead Sea: high salt → high density → easy floating