Newton's First Law of Motion — Inertia (NCERT 4.1–4.4)
1. What Does the First Law Claim?
Newton's first law states: a body continues in its state of rest or of uniform motion in a straight line unless compelled by an external unbalanced force to change that state. Every word carries weight. "Continues" asserts that motion needs no cause — the revolutionary idea of the whole scientific revolution. "State of rest or uniform motion in a straight line" quietly asserts that rest and uniform motion are the same physical situation viewed from different inertial frames, the insight this chapter inherits from relative velocity in Chapter 2. And "unbalanced" reminds you that forces routinely cancel — it is the net force that commands acceleration. The law also hands physics its working definition of force: whatever changes a body's state of motion, and its definition of inertia: the resistance every body offers to such change, measured by mass.
This page merges four short NCERT sections (4.1–4.4) because they form one argument: Aristotle guessed wrong about motion, Galileo's experiment corrected him, and Newton wrote the corrected rule as a law. Exams test the argument's steps as often as the law's statement — assertion–reason items love pairing "passengers fall forward when a bus stops" with "inertia of motion", and match-the-column items test whether you can name which everyday event demonstrates which type of inertia.
2. Complete Theory: From Aristotle's Fallacy to the First Law
Aristotle's fallacy. Aristotle held that an external force is required to keep a body moving with uniform velocity — a claim that matches daily experience, since carts stop rolling when the horse stops pulling. The hidden assumption was that friction does not exist. In reality every terrestrial body is opposed by friction and drag, so the "keeping force" Aristotle observed was merely cancelling them: push with exactly the friction force and the cart moves uniformly; stop pushing and friction alone remains, decelerating it. The correct reading — force is needed to change motion, and on Earth an equal opposing force is needed to maintain it against friction — had to wait sixteen centuries. NTA tests this history as a conceptual MCQ: the answer is always that Aristotle was misled by friction, not that his laws failed in application.
Galileo's law of inertia. Galileo imagined a ball rolling down one incline and up a smoothly joined opposite incline, reaching (nearly) its starting height. Make the second incline shallower and the ball travels farther to reach the same height; make it horizontal and the ball runs forever, since no finite distance can restore a height it never loses. Extrapolating to zero friction, a body on a horizontal plane moves with constant velocity forever — no force required. This is the law of inertia: the state of rest and the state of uniform motion need no cause; only changes of state do. Newton's first law is this conclusion promoted to a universal law, with "unbalanced external force" as the sole licensed agent of change.
The three faces of inertia — and momentum. Inertia shows up as inertia of rest (dust leaves a shaken carpet; the bus starting throws standing passengers backward; a tablecloth whipped from under dishes), inertia of motion (braking bus throws passengers forward; a moving train needs brakes and distance to stop; you jump forward from a moving step to match your old velocity), and inertia of direction (a car skids outward on a sharp turn; sparks from a grinding wheel fly tangentially; water flies off a spinning umbrella). Mass measures all three: the momentum p = mv is the "quantity of motion" a body carries, and a body with large momentum resists being stopped. Note the precision NTA exploits: momentum is a vector along v, so equal momenta can hide very different kinetic energies — the truck–bus comparison in Example 2 below makes the point numerically.
First law inside the second? Put F = 0 in the second law F = dp/dt and momentum is conserved — constant velocity. So the second law contains the first mathematically. But the first law is not redundant: it defines the inertial frames in which the second law holds, and it defines force in the first place. Frame-first, measure-second is the exam-safe ordering.
3. Visualising Galileo's Experiment
Figure 4.1 — Galileo's double incline: shallower means farther, horizontal means forever
Read the three cases left to right: the ball always tries to regain its starting height; remove the uphill (case 3) and nothing can ever stop it.
Exam read-out: in the limit of zero friction the ball never stops on the horizontal plane — motion is a state, not a process. Every "which law explains the passenger lurching…" question is this figure applied to a bus.
4. Solved Examples
Example 1 — Inertia quantified: the braking bus
A bus travelling at 18 m/s brakes to rest with a deceleration of 3 m s⁻². A standing passenger of mass 60 kg grips a horizontal handle. What horizontal force must the handle exert on him to keep him moving with the bus, and what does the answer teach about inertia?
Solution (step by step): Left alone (inertia of motion), the passenger would keep moving at 18 m/s while the floor slows under him — hence the forward lurch. To share the bus's acceleration he needs a net force F = ma = 60 × 3 = 180 N backward from the handle. The mass in F = ma is the inertia: a 90 kg passenger would need 270 N from the same handle. Dimensional check: [F] = M L T⁻² ✓, consistent with Chapter 1's dimensional table.
Example 2 — Equal momentum, unequal kinetic energy
A 1000 kg truck moves at 20 m/s and a 2000 kg bus moves at 10 m/s. Compare their momenta and kinetic energies.
Solution: ptruck = 1000 × 20 = 20 000 kg m s⁻¹; pbus = 2000 × 10 = 20 000 kg m s⁻¹ — equal momenta. But Ktruck = ½ × 1000 × 20² = 2 × 10⁵ J while Kbus = ½ × 2000 × 10² = 1 × 10⁵ J. Same "quantity of motion", twice the energy — because K = p²/2m, so at equal p the lighter body carries more kinetic energy. Momentum answers "how hard to stop the motion?", energy answers "how much work to stop it?" — the distinction is exercised heavily in momentum-conservation problems.
5. Practice Questions
Q1. A 50 kg passenger stands in a bus that starts from rest with acceleration 2 m s⁻². Which force keeps him accelerating with the bus, and what is its magnitude?
ANSWER: Friction from the floor of the bus (his feet push backward on the bus; the third-law partner pushes him forward). Magnitude F = ma = 50 × 2 = 100 N. If friction were suddenly zero (wet floor), no horizontal force would act and he would remain at rest in the ground frame — sliding backward relative to the bus.
Q2 (MCQ). Dust is removed from a hanging carpet by beating it with a stick because: (a) the dust experiences a forward force (b) the carpet moves but the dust tends to remain at rest due to inertia (c) the stick pushes the dust out (d) gravity pulls the dust out
ANSWER: (b) — the carpet jerks into motion; the dust, preferring its state of rest (inertia of rest), is left behind and falls under gravity. Option (c) is the Aristotle-flavoured distractor.
Q3. State which type of inertia operates in each case: (i) a passenger lurches forward when the driver brakes hard; (ii) a coin dropped from a moving train lands ahead of the drop point relative to the ground track; (iii) wet clothes are dried by spinning them fast.
ANSWER: (i) inertia of motion — the body continues at the bus's speed while the feet stop; (ii) inertia of motion in the horizontal direction — the coin keeps the train's horizontal velocity while falling; (iii) inertia of direction — water drops leave the cloth tangentially because their direction cannot bend without a force (surface tension's pull is overcome by spin).
6. Key Formulas & Takeaways
| Relation / statement | Condition / remark |
|---|---|
| First law: v = constant (including rest) if Fnet = 0 | Defines force and inertia; holds in inertial frames |
| Inertia ∝ mass | Mass is the quantitative measure of inertia |
| p = mv | Momentum: vector along v; SI unit kg m s⁻¹ |
| K = p²/2m | Equal momenta → lighter body has more kinetic energy |
| Aristotle: force needed to keep moving — FALSE | True only because friction exists; Galileo's inclines refute it |
| F = 0 in second law ⇒ first law | First law defines the frame; second law measures the force |
The first law is a filter, not a formula: before any F = ma work, ask "is the frame inertial and what is the net force?" — the free-body-diagram page turns that filter into a five-step routine.
7. Frequently Asked Questions
State Newton's first law of motion.
A body continues in its state of rest or of uniform motion in a straight line unless it is compelled by an external unbalanced force to change that state. The first law defines force as the agent that changes a body's state of motion, and it defines inertia: matter resists any change in its velocity. No net force means no acceleration — velocity stays constant in both magnitude and direction.
What is inertia, and what are its types?
Inertia is the inherent property of a body by which it resists any change in its state of rest or of uniform motion. It is measured by mass — greater mass means greater inertia. Its three types are: inertia of rest (a body at rest stays at rest, so passengers jerk backward when a bus starts), inertia of motion (a moving body keeps moving, so passengers lurch forward when a bus brakes), and inertia of direction (a body resists changes to its direction of motion, which is why vehicles skid on sharp turns and mud flies off tangentially from a spinning wheel).
Why was Aristotle's idea about motion wrong?
Aristotle claimed that an external force is required to keep a body moving with uniform velocity. He was misled by everyday experience: on Earth every moving body encounters friction and air resistance, so some force is indeed needed to cancel them. The flaw is that he treated these hidden opposing forces as nonexistent. Galileo showed that on a frictionless surface no force is needed to maintain motion — a body would glide forever at constant velocity. Force changes motion; it does not sustain it.
Is the first law contained in the second law?
Mathematically yes: the second law F = dp/dt with F = 0 gives dp/dt = 0, so momentum p = mv is constant, which for constant mass means constant velocity — exactly the first law's content. But the first law is not redundant, because it defines the reference frame in which the second law is valid (an inertial frame) and it defines what force means. The second law then quantifies that definition. Exams phrase this as a statement question, and the safe answer is that the first law selects the frame; the second law measures the force within it.
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