Force and Laws of Motion — Class 9 (CBSE)

Galileo started physics. Isaac Newton finished it — or rather, finished the first chapter. In 1687 he published Philosophiae Naturalis Principia Mathematica, in which three laws explain why every object on Earth (and in the solar system) moves the way it does. This chapter is those three laws, derived, proven, and applied.

1. The story — overturning 2000 years of Aristotle

Aristotle (~350 BCE) said: "Heavy objects fall faster than light ones. Motion requires a continuous push; without push, objects naturally come to rest." For 2000 years, this was the standard view in Europe.

Galileo dropped balls from the Leaning Tower of Pisa (~1590) and showed they hit the ground at the same time regardless of mass. He rolled balls down inclined planes and observed: without friction, an object in motion stays in motion indefinitely. The "natural state" isn't rest — it's UNIFORM MOTION.

Newton built on Galileo and turned it into three universal laws:

1. First law (law of inertia): an object stays at rest, or in uniform motion, unless acted upon by a net external force.
2. Second law: $F=ma$. Force = mass × acceleration. Quantitative.
3. Third law: every action has an equal and opposite reaction.

Three sentences. They describe the motion of a falling apple, a moon orbiting Earth, a rocket lifting off, a bullet recoiling, a fish swimming, a car turning. Master them and the universe becomes predictable.

2. What is a force?

A force is a push or a pull that:

• Can change the state of motion of an object (start, stop, speed up, slow down, change direction).
• Can change the shape of an object (squish, stretch, bend).
• Can change the size of an object (compress a spring).

SI unit: newton (N). One newton is the force that accelerates a 1 kg mass at 1 m/s².

$1\text{N}=1\text{kg}\cdot {\text{m/s}}^2$

Force is a vector — has magnitude and direction.

Types of forces (preview)

• Contact forces: friction, tension, normal force, applied force, spring force.
• Non-contact forces: gravity, magnetism, electric force.

3. Balanced and unbalanced forces

When multiple forces act on a body, what matters is the net force (vector sum of all forces).

Balanced forces

Net force = 0. The body's motion does NOT change.

• A book on a table: gravity pulls down ($mg$), the table pushes up (normal force). They cancel. Book stays put.
• A tug-of-war with no winner: equal pulls from both sides.

Balanced forces can CHANGE the shape of an object (a soft ball squished from both sides), but not its motion.

Unbalanced forces

Net force ≠ 0. The body accelerates (changes speed or direction).

• Push a stationary ball; it starts moving.
• Brake a moving car; it slows down.

The unbalanced force causes the change in motion. Equal magnitudes from both sides would have made the ball stay still.

4. Newton's first law — inertia

An object continues in its state of rest or of uniform motion in a straight line, unless acted upon by a net external force.

This is the formal statement. The first law has two parts:

1. A body at rest stays at rest (no force, no movement).
2. A body in uniform motion stays in uniform motion (no force, no stopping or speeding up).

Inertia

Inertia is the property of a body to resist a change in its state of motion. Higher mass = higher inertia. A truck has more inertia than a bicycle.

Mass IS a measure of inertia. A heavier object is harder to start (or stop) moving.

Three kinds of inertia

1. Inertia of rest — a body at rest tends to stay at rest. Example: when a bus suddenly starts, passengers jerk backward (their bodies were at rest and resist starting motion).

2. Inertia of motion — a body in motion tends to stay in motion. Example: when a moving bus suddenly stops, passengers jerk forward (their bodies were in motion and resist stopping).

3. Inertia of direction — a body moving in a straight line tends to keep moving in a straight line. Example: when a car takes a sharp turn, passengers feel thrown to the outside (their bodies want to keep going straight).

Seat belts are designed around these — they apply the necessary force to overcome the passenger's inertia during sudden acceleration, braking, or collision.

5. Newton's second law — F = ma

The most-used equation in mechanics.

Momentum — a new quantity

Newton actually phrased the second law in terms of momentum ($p$), defined as:

$p=mv$

Where $m$ is mass (kg) and $v$ is velocity (m/s). Momentum is a vector. SI unit: kg·m/s.

A heavy slow truck and a light fast bullet can have the same momentum — momentum captures "quantity of motion" combining both mass and speed.

The law — formally

The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction of the force.

Symbolically:

$F\propto \frac{\Delta p}{\Delta t}$

With the constant of proportionality set to 1 by the choice of SI units:

$F=\frac{\Delta p}{\Delta t}=\frac{m\Delta v}{\Delta t}=m\cdot \frac{\Delta v}{\Delta t}=ma$

The famous result:

$\boxed{F=ma}$

What this means

• A bigger force → bigger acceleration (for a given mass).
• A bigger mass → smaller acceleration (for a given force).
• Force and acceleration are in the SAME direction (both vectors, parallel).

Examples

Hitting a cricket ball: ball comes at you at 30 m/s, leaves your bat at 50 m/s. If the ball is 0.16 kg and contact lasts 0.001 s, force = m(v-u)/t = 0.16 × (50-(-30))/0.001 = 12800 N. (Note: take incoming as negative since direction reverses.)

Stopping a moving car: brakes apply force, mass × decel = stopping force. Heavy car + same braking system → longer stopping distance. That's why trucks need bigger brakes than cars.

6. Newton's third law — action and reaction

To every action, there is an equal and opposite reaction.

Forces always come in pairs. When body A pushes body B with force $F$, body B pushes back on A with $-F$ (same magnitude, opposite direction).

Important: action and reaction act on DIFFERENT bodies

• You push a wall (action on wall); wall pushes back on you (reaction on YOU).
• A rocket pushes hot gas downward (action on gas); the gas pushes the rocket upward (reaction on rocket) → rocket lifts off.
• You walk forward by pushing the ground backward (action on ground); the ground pushes you forward (reaction on you).
• A swimmer pushes water backward (action on water); water pushes swimmer forward (reaction on swimmer).

Why action and reaction don't cancel

They act on DIFFERENT bodies, so they don't cancel each other. (Forces on the SAME body would cancel.)

This is the most common Class 9 question conceptual error. If a horse pulls a cart with force $F$ and the cart pulls back with $-F$, why does the cart move? Because:

• $F$ on the cart causes the cart to accelerate (it's an unbalanced force on the cart, given its weight + friction).
• $-F$ on the horse does NOT prevent the horse from accelerating — the horse separately pushes the ground backward, and the ground reaction pushes the horse forward.

7. Law of conservation of momentum

A direct consequence of Newton's third law: in a closed system (no external forces), the total momentum is conserved.

$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$

This applies before and after any collision or explosion — for any two-body interaction in an isolated system.

Derivation (brief)

By Newton's 3rd law, the force on body 1 from body 2 equals minus the force on body 2 from body 1. By Newton's 2nd law, force = rate of change of momentum. So $\Delta p_1=-\Delta p_2$, meaning $\Delta p_1+\Delta p_2=0$. Total momentum is constant.

Applications

1. Rocket propulsion: rocket ejects hot gas backward (gas gains momentum in one direction); rocket gains equal and opposite momentum (forward). $0=m_{\text{gas}}{v}_{\text{gas}}+m_{\text{rocket}}{v}_{\text{rocket}}$ → $v_{\text{rocket}}=-m_{\text{gas}}{v}_{\text{gas}}/m_{\text{rocket}}$.

2. Recoil of a gun: gun + bullet at rest; bullet fires forward with high velocity → gun recoils backward. Momentum conservation: $0=m_b{v}_b+m_g{v}_g$, so $v_g=-m_b{v}_b/m_g$. Small mass × big velocity for the bullet = big mass × small velocity for the gun.

3. Collision of two cars: total momentum before = total momentum after, regardless of whether the collision is elastic, inelastic, or partial. (Energy may or may not be conserved; momentum always is.)

8. Impulse — change in momentum

When a force acts on a body for a short time, the resulting change in momentum is called impulse.

$\text{Impulse}=F\times t=\Delta p=m(v-u)$

SI unit: N·s (or equivalently kg·m/s, same as momentum).

Examples

• A catcher pulls his hands back when catching a cricket ball: extends the contact time $t$ → reduces the force experienced (impulse is fixed).
• Air bags in cars: extend the time of impact during collision → reduce the force on the passenger.
• Boxer rolling with a punch: extends contact time → reduces force.

For a fixed change in momentum, a longer time means a smaller force. Useful in many safety designs.

9. Worked example — recoil of a gun

A gun of mass 5 kg fires a bullet of mass 50 g with a velocity of 200 m/s. Find the recoil velocity of the gun.

Step 1 — Identify before and after.

• Before: gun + bullet at rest. Total momentum = 0.
• After: bullet moves at 200 m/s forward; gun recoils at velocity $v$ (find this).

Step 2 — Convert units. Bullet mass = 50 g = 0.05 kg. Gun mass = 5 kg.

Step 3 — Apply conservation of momentum. $0=(0.05)(200)+(5)(v)$ $0=10+5v$ $v=-2\text{m/s}$

The negative sign means the gun recoils in the direction opposite to the bullet's motion.

Answer: The gun recoils at 2 m/s backward.

10. Closing thought

You started this chapter knowing forces push and pull. You're ending it with the three laws that govern the motion of every object in every direction at every scale below light-speed.

Newton's laws built the modern world:

• Civil engineering uses them for bridges and buildings.
• Mechanical engineering uses them for engines and turbines.
• Aerospace engineering uses them for planes and rockets.
• Sports science uses them to optimise human performance.
• Medical engineering uses them for prosthetics, cardiac modeling, MRI design.

In 1687 they were three sentences. In 2026, they're the working tools of millions of engineers worldwide. That's how good physics travels through time.