Newton’s Laws and Free-Body Diagrams: Mastering the Rules of Motion
JEE/NEET Physics · Laws of Motion series · Part 1 of 8 · All parts →
- First law: no net force → velocity never changes (rest stays rest, motion stays motion)
- Second law: F_net = ma — net force is the ONLY producer of acceleration
- Third law: forces come in pairs, equal and opposite, on DIFFERENT bodies
- The FBD: draw ONE body, draw only the forces ON it — the method that solves everything
- Inertia is mass’s resistance to velocity-change: more mass, same force, less acceleration
Everything you’ll ever study in mechanics is contained in three sentences a 37-year-old Englishman named Isaac Newton wrote in 1687 in his Principia Mathematica. Missiles, muscles, moon missions — all consequences of Newton’s three laws. Part 1 of the Laws of Motion series — the highest-weightage chapter of Class 11, and the foundation on which every later topic (friction, circular motion, work-energy, rotations) is built.
- The first law: the law of laziness
- The second law: the cause of change
- The third law: the law of pairs
- The FBD: physics’s single best tool
- Solved examples
- Common mistakes
- This physics in your daily life
- Practice set
- Recap
- Frequently asked questions
The First Law: The Law of Laziness
Things don’t like change. With zero net force, a resting object rests forever, and a moving object cruises at constant velocity — same speed, same direction — forever. Motion needs no cause; only changes in motion do. This single sentence overturned 2000 years of Aristotle’s physics (‘things need pushes to keep moving’) — they don’t; friction simply hides the truth by quietly robbing moving objects of their speed.
Newton’s genius was spotting that a sliding book slows down not because “motion naturally dies” but because an invisible force (friction) acts on it. Remove the friction — as Galileo demonstrated with increasingly smooth inclined planes, and as we can see perfectly in empty space — and motion continues without any push at all. The natural state of an object is not rest; it is whatever velocity it currently has.
This laziness has a name: inertia. And inertia is measurable — it’s mass. A loaded truck is “lazier” than a bicycle: the same braking force changes the bicycle’s motion dramatically and the truck’s barely at all. Note carefully that the first law is not just “rest stays at rest” — the equally important half is that uniform motion also persists. Both halves are JEE/NEET favourites.
The Second Law: The Cause of Change
| Letter | What it means (plain words) | Value / unit |
|---|---|---|
| F_net | the VECTOR SUM of all forces on the body | newtons (N) |
| m | the mass — the laziness rating | kg |
| a | the acceleration produced | m/s², same direction as F_net |
Double the net force → double the acceleration. Double the mass → half the acceleration. It’s a recipe with three ingredients, and it’s why mass is called inertia: the measure of a body’s refusal to change its velocity.
Two subtleties examiners love to test. First, the law is a vector equation — it really says F(net,x) = ma(x) and F(net,y) = ma(y) separately. You can have a huge force in x and zero acceleration in y; the axes never mix. Second, the more fundamental form is F = dp/dt (force = rate of change of momentum). For constant mass this reduces to F = ma, but in problems with changing mass (rockets, conveyor belts, sand leaking from a cart) the momentum form is the one that survives. We’ll meet it again in Part 7.
Units check, since one mark often hides here: 1 newton = 1 kg · m/s². A force of 1 N changes the velocity of a 1 kg mass by 1 m/s every second — a small, everyday-sized push, roughly the weight of a 100-gram apple.
The Third Law: The Law of Pairs
You push the wall; the wall pushes you back, equally hard, oppositely directed — and crucially, on different bodies. That’s why the pair doesn’t cancel: they act on different victims. Walk, swim, rocket-launch: every ‘push off something’ in the universe is third law.
The precise wording matters: if body A exerts a force on body B, then body B exerts an equal and opposite force on body A. “Equal” means equal in magnitude — always, regardless of the masses involved. When a truck collides with a fly, the truck pushes the fly and the fly pushes the truck with exactly the same force. The fly’s fate is worse only because the same force produces a huge acceleration on a tiny mass (second law) and a negligible one on the truck.
Also note that action and reaction are always of the same type: friction pairs with friction, normal pairs with normal, gravity pairs with gravity (the Earth pulls you down; you pull the Earth up). If you find yourself pairing “gravity on me” with “normal on me”, you’ve made a classic error — those are two different interactions acting on one body, not a third-law pair.
The FBD: Physics’s Single Best Tool
The free-body diagram isolates ONE body, strips everything else away, and draws only the arrows of force acting ON it. Weight down, normal up, tension along the rope, friction along the surface. Then F_net = ma per axis. Every problem in this series begins with an FBD — no exceptions.
Here is the reliable four-step recipe to apply in every problem:
Step 1 — Choose the body. Pick the one object whose motion you care about, and imagine chiselling it out of the scene. Everything else becomes “the rest of the universe”, represented only by the forces it exerts on your body.
Step 2 — Draw all forces ON it, and only those. Ask at every contact point and every distance-interaction: does something touch it (normal, tension, friction)? Does something pull across empty space (gravity)? Each yes gets exactly one arrow. Never draw the force your body exerts on something else — that arrow belongs to someone else’s FBD.
Step 3 — Choose axes and resolve. Align one axis with the expected acceleration (usually along the motion) and resolve every force into components. On the perpendicular axis, a = 0, so forces simply balance.
Step 4 — Write F = ma per axis and solve. Unknowns become algebra. If the equations don’t close, you’ve either missed a force or drawn a phantom one — recheck the contacts.
Treat the FBD as a translation step: physics sentences (blocks, ramps, ropes) get translated into the language of arrows, and once the translation is right, the rest is arithmetic. Nearly every wrong answer in this chapter traces back to a wrong FBD, not to bad algebra.
Solved Examples
Only one horizontal force acts, so the net force is 20 N. From the second law:
a = F/m = 20/5 = 4 m/s², in the direction of the push.
✔
Answer: 4 m/s²
Forces along the same line combine by subtraction:
F_net = 10 − 4 = 6 N → a = 6/2 = 3 m/s² right.
Only the NET force accelerates — the individual forces merely argue. ✔
Answer: 3 m/s²
Draw the man’s FBD: normal N up, weight 60 × 10 = 600 N down. He is in equilibrium, so:
Man: N (platform’s push up) − 600 = 0 → N = 600 N.
By the third law the man pushes the platform DOWN with 600 N too — same pair, different bodies. (The platform’s 40 kg mass is extra information, a favourite examiner trick: the man–platform interaction depends only on the man’s weight here.)
600 N — the pair never cancels because it never acts on one body. ✔
Answer: 600 N (action-reaction pair)
- ‘Motion needs a force.’ No — CHANGE of motion needs a force; constant velocity is free (first law).
- Adding action-reaction pairs into one FBD. The pair acts on the OTHER body — your FBD contains only forces on YOUR body.
- Using F = ma with any single force. Only the net force enters; subtract opposing forces first.
- Weight vs mass confusion. Mass (kg) is laziness; weight (mg, newtons) is gravity’s pull on it — related but different animals. Mass is the same on the Moon; weight is not.
- ‘Heavier objects fall faster.’ In free fall, doubling m doubles the gravitational force AND doubles the laziness — the effects cancel, so a is g for everyone (ignoring air resistance).
- Assuming N always equals mg. The normal force takes whatever value the situation demands — in an accelerating lift it can be more or less than mg. Never preset it; solve for it.
This Physics in Your Daily Life
- Seatbelt versus windshield — the car stops; your body obeys the first law and keeps going at 50 km/h until something supplies the stopping force. The belt volunteers.
- You ‘fall forward’ when the bus brakes — no mystery force: your body simply continued, per the first law, while the bus slowed beneath it.
- Every step you take — you push the Earth backwards; the Earth pushes you forwards (third law). You move; the Earth’s change is unmeasurably small (its mass is unmeasurably big).
- Rockets work in empty space — nothing to push against? They push their own exhaust backwards; exhaust pushes them forwards. Third law needs no ground.
- Shopping-trolley physics — a full trolley accelerates lazily, an empty one zooms: same push, different mass, F = ma at the supermarket.
- Karate board breaks — the hand delivers a large force in a short time; by the second law the board’s pieces acquire large accelerations, exceeding the board’s breaking strength.
- Wet dog shake — rapid back-and-forth motion of the body gives water droplets large accelerations; the weak surface-tension grip can’t provide the needed force, so the drops fly off (first/second law teamwork).
Aristotle thought a moving arrow needed a continuous push. Galileo stared at ice pucks and suspected laziness instead; Newton wrote it as law: the universe’s default is ‘keep doing whatever you’re doing’. Pushes don’t cause motion — they cause CHANGES. The arrow flies because nothing stops it yet.
Same 100 N push on a 50 kg cart and a 1000 kg car: a = 2 m/s² versus 0.1 m/s² — same force, tenfold difference in obedience. And a 1000 kg car braking at 5 m/s² needs exactly F = 5000 N of friction, always, no exceptions: the recipe never lies.
Draw the FBD: the body as a dot, arrows radiating outward — weight down, normal up, applied pushes, friction opposing. Circle the net arrow per axis. Every mechanics problem, from pencil to spacecraft, is this same picture with different arrow labels.
Practice Set (Answers Hidden — Try First)
(NEET-level) 10 N on 4 kg (frictionless): a =
(JEE Main-level) Net of 15 N right, 5 N left on 2 kg: a =
(NEET-level) A body moves at constant velocity. Net force =
(Concept) Action and reaction cancel each other when:
(JEE Main-level) 2 kg at 3 m/s² needs net force:
(JEE Advanced-style thought) A fly hits a truck head-on. Compare the forces each experiences.
- 1st: no net force → velocity constant forever
- 2nd: F_net = ma, same direction
- 3rd: pairs act on different bodies — never cancel
- FBD: one body, only forces ON it
- mass = inertia = resistance to change
- 1 N = 1 kg·m/s² (apple-weight-sized push)
- 🔁 three laws in one line each: “lazy, recipe, pairs”
- 🔁 F_net = ma per axis
- 🔁 action-reaction on different bodies
Frequently Asked Questions
Q. If the net force is zero, are there no forces acting?
A. Not necessarily — forces may act but balance perfectly. A book on a table has weight and normal force on it; their sum is zero, so a is zero. Zero net force, not zero force.
Q. Is the first law contained in the second?
A. Formally, F = 0 gives a = 0, so yes mathematically. But historically and conceptually the first law stands alone: it defines inertial frames — the special reference frames in which the second law is even valid. That’s why it earns its own place.
Q. If action and reaction are always equal, how does anything ever move?
A. Because the two forces act on different bodies. When you walk, the reaction pushes you forward while the action decelerates the Earth — the forces never need to cancel, since cancellation only matters for forces on the same body.
Q. Can acceleration exist without velocity?
A. Yes — at the top of a vertically thrown ball’s flight, v = 0 but a = g downward (gravity never pauses). Velocity is where you are heading; acceleration is how fast that heading changes.
- 🧠 Chant: ‘lazy, recipe, pairs’ — first, second, third laws in three words.
- 🧠 FBD rule: ‘one body, all arrows in, nothing else’.
- 🧠 Units: 1 N = 1 kg·m/s²; mass in kg, weight in N (w = mg).
- 🏠 Daily: bus-brake lurch = first law in your face.
- 🏠 Daily: walking is pushing the Earth backwards.
Quick revision
- First law: no net force → velocity never changes (rest stays rest, motion stays motion)
- Second law: F_net = ma — net force is the ONLY producer of acceleration
- Third law: forces come in pairs, equal and opposite, on DIFFERENT bodies
- The FBD: draw ONE body, draw only the forces ON it — the method that solves everything
- Inertia is mass’s resistance to velocity-change: more mass, same force, less acceleration
- The first law: the law of laziness
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