Newton's First Law and Inertia

Newton’s First Law and Inertia

🟢 Lite — Quick Review (1h–1d)

Newton’s First Law (Law of Inertia): A body continues in its state of rest or uniform motion unless an external force acts on it. Inertia is the resistance of any physical object to a change in its state of motion.
Newton’s Second Law: Net force equals mass times acceleration: F = ma, where F is in newtons (N), m in kilograms (kg), and a in m/s². Impulse J = FΔt = Δp, linking force and change in momentum.
Newton’s Third Law: Every action has an equal and opposite reaction — the forces act on different bodies simultaneously.
Momentum: p = mv (kg·m/s). Momentum is conserved in an isolated system.
Friction: f = μN. Static friction ≤ μₛN; kinetic friction = μₖN. μₛ > μₖ always.
TNPSC Quick Pointers: (1) Weight = mg (g = 9.8 m/s²), not equal to mass. (2) Normal force N ≠ mg on inclined planes — N = mg cos θ. (3) Friction opposes impending motion, not motion direction in all cases.

🟡 Standard — Regular Study (2d–2mo)

1. Newton’s First Law and Inertia

A body at rest stays at rest; a body in motion continues with constant velocity unless an external force acts. This property of matter resisting changes in its state of motion is called inertia. Mass is the quantitative measure of inertia — a heavier object has greater inertia and requires more force to change its state.

2. Newton’s Second Law (F = ma)

The acceleration of a body is directly proportional to the net force acting on it and inversely proportional to its mass. The direction of acceleration is the same as the direction of the net force. Impulse is the product of force and the time interval during which it acts: J = FΔt = Δp. This theorem explains why padded dashboards reduce injury — extending the time of impact reduces the average force.

3. Newton’s Third Law (Action-Reaction)

Forces always occur in pairs: body A exerts a force on body B, and body B exerts an equal and opposite force on body A. These two forces act on different objects — they never cancel each other out even though they are equal in magnitude and opposite in direction.

4. Friction

The force of friction f = μN, where μ is the coefficient of friction and N is the normal force. Static friction prevents motion up to a maximum value fₛ(max) = μₛN. Kinetic friction acts during motion: fₖ = μₖN. Since μₛ > μₖ, more force is needed to initiate motion than to sustain it.

5. Momentum Conservation

In an isolated system with no external forces, the total momentum before and after any interaction remains constant: Σp_initial = Σp_final. This principle governs collisions, rocket propulsion, and recoil of guns.

🔴 Extended — Deep Study (3mo+)

Deriving F = ma from Momentum

Newton’s original statement in the Principia reads: “The change of motion is proportional to the applied force.” “Motion” meant what we now call momentum (p = mv). The modern form follows directly:

$$\vec{F}_{net} = \frac{d\vec{p}}{dt} = \frac{d(m\vec{v})}{dt}$$

For constant mass (non-relativistic regime), this reduces to F = ma since m is constant and d(v)/dt = a. This derivation matters in TNPSC because examiners sometimes ask why F = ma holds only for constant-mass systems — it breaks down for rockets expelling fuel, where mass changes.

Equilibrium and Free-Body Diagrams

A body is in translational equilibrium when ΣF = 0, meaning it has zero net acceleration (at rest or moving at constant velocity). Drawing a free-body diagram (FBD) is essential: identify every force acting on the body, resolve into components, and apply ΣFₓ = 0, ΣFᵧ = 0. A common mistake is including forces that act on other bodies in the same FBD — action-reaction pairs belong on separate diagrams.

Circular Motion — Centripetal Force

For an object moving in a circle of radius r with speed v, the required centripetal force is F_c = mv²/r, directed toward the centre. This is not a new force — it is whatever net force (tension, friction, gravity) provides the inward pull. If the required centripetal force exceeds available force (e.g., friction μN), the object leaves the circular path (skids).

Common Mistakes to Avoid

Trap	Why It’s Wrong
Weight = mass	Weight is a force (W = mg ≈ 9.8m N on Earth); mass is constant and scalar.
Normal force always = mg	On an incline, N = mg cos θ; on a vertical wall, N = horizontal component.
Friction opposes motion	Friction opposes relative motion or impending motion — a car moving forward has friction from the road pushing it forward.
Action-reaction forces cancel	They act on different bodies, so they never cancel each other.

TNPSC Exam Strategy

Laws of Motion typically yields 1–3 MCQs in Prelims covering F = ma calculations, friction on inclined planes, and impulse-momentum problems. Mains General Science questions ask for explanations — be ready to explain braking distance, why a passenger lurches forward when a vehicle suddenly stops (inertia), and how a rocket works in space with no air (action-reaction). The weightage is roughly 3–5% of the Science paper.

Practice Prompts

A 5 kg block rests on a rough horizontal surface (μₛ = 0.4, μₖ = 0.3). (a) What minimum horizontal force initiates motion? (b) If the same force continues after motion begins, what is the acceleration? [Ans: (a) F_min = μₛN = 0.4 × 49 = 19.6 N; (b) fₖ = μₖN = 0.3 × 49 = 14.7 N; a = (19.6 − 14.7)/5 = 0.98 m/s²]
A 60 kg person jumps from a height and lands stiff-legged, experiencing an impulse of 1800 N·s over 0.1 s. What average force acts? Is this safer than landing with bent knees (Δt = 0.4 s)? [Average force = 1800/0.1 = 18,000 N vs 1800/0.4 = 4,500 N — bent knees reduce force by 75%.]

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