Force
A push or pull on an object that can change its state of rest or motion, or change its shape and size. Force has both magnitude and direction — it is a vector quantity.
Inertia
The natural tendency of an object to resist any change in its state of motion or rest. A body at rest stays at rest; a body in motion stays in motion — unless acted upon by a force.
Momentum (p)
The quantity of motion an object possesses. Defined as p = m × v (mass × velocity). It is a vector quantity with the same direction as velocity. SI unit: kg·m/s.
Balanced Forces
When two or more forces acting on an object are equal and opposite, they cancel out (net force = 0). The object does not accelerate — it stays at rest or moves at constant velocity.
Unbalanced Forces
When the net force on an object is not zero. This causes a change in velocity (acceleration). The object moves in the direction of the larger force.
Friction
A contact force that always opposes motion (or impending motion) between two surfaces. Acts opposite to the direction of relative motion. Cannot be completely eliminated.
Impulse
The product of force × time (F × t). Impulse equals the change in momentum of a body. Useful when a large force acts for a very short time (e.g., bat hitting a ball).
Conservation of Momentum
In an isolated system (no external forces), the total momentum before an event equals total momentum after. Momentum is never created or destroyed.
Acceleration
The rate of change of velocity. Produced when an unbalanced force acts on an object. Direction of acceleration = direction of the net force. Formula: a = (v−u)/t.
Types of Forces at a Glance
Inertia and Mass — Visual Comparison
Real-World Connection — Seat Belts & Inertia
When a car brakes suddenly, your body tends to keep moving forward — this is inertia in action. The seat belt exerts a backward force on you to slow you down safely. Without it, you'd continue moving and hit the dashboard. Every safety feature in a vehicle is designed to manage Newton's First Law!
Did You Know? — Galileo's Experiment
Galileo Galilei (1564–1642) was the first to challenge Aristotle's ancient idea that "objects need force to keep moving." Galileo rolled a ball on a smooth inclined plane and observed that if friction were removed entirely, the ball would roll forever on a flat surface. This became the basis of Newton's First Law — over 1500 years of wrong thinking, corrected by one clever experiment!
Newton's First Law — Law of Inertia
Named by Isaac Newton · Published 1687 · Based on Galileo's observations
In simpler terms: Objects don't change their motion on their own. If net external force = 0, then acceleration = 0. The object either stays still or moves in a straight line at constant speed forever.
Inertia of Rest
A stationary object remains stationary. When you shake a tree, the tree moves but fruits (being separate objects) tend to stay — they fall down due to this lag.
Inertia of Motion
A moving object tends to keep moving. A passenger in a braking bus lurches forward because their body wants to keep moving at the bus's original speed.
Inertia of Direction
A moving object resists change in direction. When a car turns sharply, you slide to the outer side — your body wants to keep going straight.
Did You Know? — Carom Coin Trick
Stack a pile of carom coins and flick the bottom coin sharply with a striker. The bottom coin flies out, but the rest of the pile drops straight down — they didn't move sideways because of their inertia of rest! This is a classic classroom demonstration of Newton's First Law.
Newton's Second Law — Law of Force & Acceleration
Quantitative law relating force, mass, and acceleration
Key insight: Doubling the force doubles the acceleration. Doubling the mass halves the acceleration (for the same force). This is why a cricket ball hurts more when it hits fast — greater momentum, greater change, greater force.
Real-World Connection — Catching a Cricket Ball
A skilled fielder pulls their hands backward while catching. This increases the time (Δt) over which the ball's momentum drops to zero — so the force experienced (F = Δp/Δt) is much smaller and doesn't hurt. This is pure Newton's Second Law in action on every cricket ground!
Newton's Third Law — Law of Action & Reaction
Every force has an equal and opposite counterpart
Action–Reaction Pairs
Common Misconception!
Action and reaction forces do NOT cancel each other — because they act on different objects. Forces can only cancel when they act on the same object. Also, there is no time gap: action and reaction are always simultaneous.
Did You Know? — You Push the Earth!
When you stand on the ground, gravity pulls you down (Earth pulling you). By Newton's Third Law, you pull the Earth upward with an equal force! The reason Earth doesn't visibly move is its enormous mass (~6×10²⁴ kg) — the acceleration it experiences is so tiny it's unmeasurable.
Law of Conservation of Momentum
Derived from Newton's Second and Third Laws
Real-World Connection — Gun Recoil
Before firing, both gun and bullet are at rest — total momentum = 0. After firing, bullet moves forward and gun "recoils" backward, so that the total momentum remains zero. A heavier gun recoils less (smaller velocity) than a lighter one. This is conservation of momentum in every gunshot ever fired.
Force = Mass × Acceleration
Momentum = Mass × Velocity
Impulse = Force × Time = Change in Momentum
Kinematics Equations
Frictional Force
Before collision = After collision (isolated system)
Exam Tip — Signs Matter!
Always define a positive direction before solving. Velocities or forces in the opposite direction should be taken as negative. This is critical for momentum problems — getting the sign wrong flips your entire answer!
| Quantity | Symbol | SI Unit | Named After | Definition / Notes |
|---|---|---|---|---|
| Force | F | N (Newton) | Isaac Newton (1643–1727) | 1 N = 1 kg·m/s² · Force that gives 1 kg an acceleration of 1 m/s² |
| Mass | m | kg | — | Measure of inertia. Not the same as weight! Mass is constant everywhere. |
| Acceleration | a | m/s² | — | Rate of change of velocity. Direction = direction of net force. |
| Velocity | v | m/s | — | Speed + direction. Vector quantity. Scalar equivalent = speed. |
| Momentum | p | kg·m/s | — | Also written as N·s. Product of mass and velocity. Vector quantity. |
| Impulse | J | N·s | — | Equivalent to kg·m/s. Equals the change in momentum. |
| Coefficient of Friction | μ | Dimensionless | — | No units. Ratio of friction force to normal force. Always between 0 and 1 (typically). |
| Weight | W | N (Newton) | — | W = mg. Weight is a force — it changes with gravity. Mass does NOT change! |
| Time | t | s (second) | — | Scalar quantity. Used in all kinematic and force calculations. |
| Displacement | s | m (metre) | — | Vector — has direction. Different from distance (scalar). |
Did You Know? — Your Weight Changes on Other Planets!
Your mass is always the same (say 60 kg) wherever you go — it measures inertia. But your weight (a force) changes: on Mars (g = 3.7 m/s²) you'd weigh 222 N; on Jupiter (g = 24.8 m/s²) you'd weigh 1488 N! Weighing scales measure force, not mass — so a spring scale reads differently on each planet.
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Car Seat Belts
When a car stops suddenly, passengers continue moving forward due to inertia (Newton's 1st Law). Seat belts apply a backward force to stop them — without it, they'd hit the windshield. Every car safety feature is Newtonian mechanics! -
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Cricket Fielder Pulling Hands Back
By increasing the time for the ball's momentum to change to zero (F = Δp/Δt), the force on the hands is reduced dramatically. Same principle applies to high-jump athletes landing on a cushion instead of concrete. -
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Rocket Propulsion
A rocket burns fuel and expels hot gases backward at high speed. By Newton's 3rd Law, the gases push the rocket forward. By conservation of momentum, the rocket gains momentum equal to what the gases carry backward. Rockets work even in empty space — no air needed to push against! -
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Walking and Running
You push your foot backward against the ground (action). The ground pushes your foot forward (reaction — Newton's 3rd Law), and you move forward. On a frictionless ice surface, you can barely walk because there's no reaction force to propel you. -
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Bowling / Billiards Collisions
When a bowling ball hits pins, total momentum is conserved. The ball slows down and pins fly — but the total momentum of the whole system (ball + pins) is the same before and after. A billiard ball hitting another at rest transfers its momentum and may stop completely. -
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Anti-lock Braking System (ABS)
ABS prevents wheels from locking up during hard braking. Locked wheels skid, reducing friction to the kinetic value. ABS keeps wheels rolling, maintaining higher static friction — stopping the car faster and more safely. It's Newton's Laws + friction science in your car's computer! -
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Ships and Anchors
A huge ship moves with enormous momentum (large mass × velocity). To stop it, a massive force is needed for a long time — this is why ships need kilometres to fully stop even after engines cut off. Anchors and friction with water supply this stopping force gradually. -
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Air Bags in Cars
Like a fielder's hands, an airbag increases the stopping time from a crash by ~10x. F = Δp/Δt — same change in momentum but much larger Δt = much smaller force on your head. This difference between ~10 ms vs ~100 ms is literally the difference between life and death. -
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Swimming
You push water backward (action). Water pushes you forward (reaction). The harder you push — and the more surface area your hand offers — the greater the reaction and the faster you swim. Competitive swimmers wear tight suits to reduce friction with water, not arms! -
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Circus Tightrope Walker
Balancing on a rope means keeping the net force and torque exactly zero (Newton's 1st Law equilibrium). The long pole carried by the walker shifts their center of gravity and slows any imbalance — giving them more time to correct. Physics is their most important skill!
Did You Know? — Astronauts and Inertia in Space
In the International Space Station, astronauts are weightless — but NOT massless. If an astronaut needs to stop a floating 200 kg crate, they still need to push hard and brace themselves. Inertia doesn't disappear in space — only gravity does. A 200 kg crate still has the same resistance to motion as on Earth. Astronauts learn this quickly (and painfully)!
🔵 Newton's Laws apply to "particles"
Strictly, Newton's laws describe point masses (particles). In practice, we apply them to rigid bodies, treating all forces as acting at the centre of mass. This works well for most everyday problems.
🔵 Non-relativistic speeds only
Newton's laws are valid for speeds much less than the speed of light (3×10⁸ m/s). At speeds approaching light, Einstein's Special Relativity must be used. For everyday motion, Newton is perfectly accurate.
🔵 Inertial reference frames
Newton's laws are valid only in non-accelerating frames of reference (inertial frames). In a rotating or accelerating reference frame (like a merry-go-round), fictitious forces like centrifugal force appear.
🔵 Massless strings and pulleys
In most school-level problems, strings and pulleys are assumed to have zero mass and zero friction. This means tension is the same throughout the string. In real life, ropes have mass and friction — but ignoring this simplifies calculations without much error.
🔵 Friction is independent of area
The friction formula f = μN assumes friction doesn't depend on the area of contact — only on the normal force and surface types. Experimentally this is approximately true for most solid surfaces. (It breaks down for soft materials like rubber.)
🔵 Constant mass
F = ma assumes mass is constant. For rockets burning fuel, mass changes — more advanced equations (Tsiolkovsky rocket equation) are needed. For all school problems, mass is treated as constant.
🔵 g is constant near Earth's surface
We assume g = 9.8 m/s² (often rounded to 10 m/s²) is constant. In reality, g varies slightly with altitude and latitude. At Mount Everest's peak, g ≈ 9.77 m/s². This variation is ignored unless specifically stated.
🔵 Air resistance is neglected
Unless stated, problems ignore air resistance (drag force). In reality, air resistance depends on speed, shape, and air density. This is why a feather and a metal ball don't fall at the same rate outside a vacuum chamber.
Important Distinction — Mass vs Weight
Mass (kg) is the amount of matter and a measure of inertia — it never changes. Weight (N) is the gravitational force on that mass — it changes with location. On the Moon, your mass is the same, but your weight is 1/6th of Earth's weight. Scales measure weight in Newtons, not mass in kilograms (though they're calibrated to show kg for convenience).
Tip — Isolating a System for Newton's 2nd Law
When solving problems with multiple bodies, draw a Free Body Diagram (FBD) for each object separately. Show all forces acting ON that object (not forces it exerts on others). Apply F = ma to each object. Use Newton's 3rd Law to link equations between objects (e.g., tension is same in both objects connected by a string over a smooth pulley).
⚡ Force Calculator (F = ma)
💨 Momentum Calculator (p = mv)
🌍 Weight vs Mass Calculator (W = mg)
💥 Impulse & Change in Momentum
Try It! — Classic Problems
Problem 1: A 5 kg object accelerates at 4 m/s². What force acts on it? (Ans: F = 5×4 = 20 N)
Problem 2: A 0.2 kg hockey ball moves at 10 m/s, then returns at 5 m/s after being hit. What is the change in momentum? (Ans: Δp = 0.2×(−5−10) = −3 kg·m/s → magnitude 3 N·s)
Problem 3: What is a 70 kg person's weight on the Moon? (Ans: W = 70×1.6 = 112 N — use the weight calculator above!)