Laws of motion — first, second, third law connections and applications

Question

State Newton’s three laws of motion. How are they interconnected? Give practical examples and explain which law applies in common JEE/NEET problem types.

Newton’s Laws Relationship Map

flowchart TD
    A["Newton's Laws of Motion"] --> B["First Law — Law of Inertia"]
    A --> C["Second Law — F = ma"]
    A --> D["Third Law — Action-Reaction"]
    B --> E["Defines what happens when F_net = 0"]
    C --> F["Defines what happens when F_net ≠ 0"]
    D --> G["Forces always come in pairs"]
    E --> H["Object stays at rest or moves with constant velocity"]
    F --> I["Object accelerates: a = F/m"]
    G --> J["Action on body A by B = Reaction on body B by A"]
    B -.->|"Special case of"| C
    C -.->|"When F=0, reduces to"| B

Solution — Step by Step

Statement: A body at rest stays at rest, and a body in uniform motion continues in uniform motion in a straight line, unless acted upon by a net external force.

What it really means: Objects resist changes to their state of motion. This resistance is called inertia, and it is proportional to mass. A heavier object is harder to start, stop, or change direction.

Examples:

When a bus suddenly brakes, passengers lurch forward — their bodies tend to continue moving (inertia of motion)
A coin on a cardboard stays in place when the cardboard is flicked away — inertia of rest
Dust flies off a carpet when you beat it — the carpet moves, dust stays behind

Key insight: The first law defines the concept of an inertial reference frame — a frame where this law holds. This is fundamental for JEE Advanced.

Statement: The net external force on a body equals the rate of change of its momentum.

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

For constant mass:

\vec{F}_{net} = m\vec{a}

What it really means: Force causes acceleration, not velocity. If you push a box with a constant force, it keeps accelerating — it does not move at constant speed. Also, $\vec{F} = m\vec{a}$ is a vector equation — you must resolve forces along x and y axes separately.

Problem-solving framework:

Draw a free body diagram (FBD)
Choose coordinate axes
Write $\Sigma F_x = ma_x$ and $\Sigma F_y = ma_y$
Solve

Statement: For every action, there is an equal and opposite reaction. If body A exerts a force on body B, then body B exerts an equal and opposite force on body A.

\vec{F}_{AB} = -\vec{F}_{BA}

Critical detail: Action and reaction act on different bodies. They never cancel each other because they are on different objects. A common confusion arises when students try to add action and reaction on the same FBD — they should not.

Examples:

You push a wall — the wall pushes you back (that is why you can feel it)
Rocket propulsion — hot gases push out (action), gases push rocket forward (reaction)
Walking — your foot pushes ground backward (action), ground pushes you forward (reaction)

The first law is a special case of the second law: when $F_{net} = 0$ , $a = 0$ , so velocity is constant (or zero). However, the first law is not redundant — it defines the concept of inertial frames, which the second law assumes.

The third law is independent — it tells us about the nature of forces (they always come in pairs), while the second law tells us what a force does to a single body.

In JEE/NEET problems:

First law: Equilibrium problems (body at rest or constant velocity — $\Sigma F = 0$ )
Second law: Acceleration problems (pulley systems, incline problems, connected bodies)
Third law: Identifying reaction forces, normal force problems, contact force between stacked blocks

Why This Works

Newton’s laws form a complete framework for classical mechanics. The first law tells you when to expect no acceleration, the second law quantifies the relationship between force and acceleration, and the third law ensures that you account for all forces correctly. Together, they can solve any mechanics problem that does not involve relativistic speeds or quantum scales.

In JEE Main, the most common application of Newton’s laws is in connected body problems — two blocks on a pulley, blocks on an incline, or stacked blocks. For all of these, the method is the same: draw separate FBDs for each body, apply $F = ma$ to each, and solve the simultaneous equations. Practise this systematically.

Alternative Method — Momentum Formulation

For problems involving variable mass (like rockets) or collisions, use the momentum form of the second law:

\vec{F} = \frac{d\vec{p}}{dt}

This is more general than $F = ma$ because it handles cases where mass changes with time.

Example: A rocket ejects mass $dm$ at velocity $v_e$ relative to the rocket. The thrust force is:

F_{thrust} = v_e \frac{dm}{dt}

Common Mistake

The biggest mistake in Newton’s third law: students think action and reaction cancel out. They do NOT, because they act on different bodies. When you draw an FBD of one block, you include only the forces acting ON that block — the reaction force acts on the other body and appears on its FBD. If action and reaction cancelled, nothing would ever accelerate! This confusion costs marks in nearly every connected-body problem.