Class 9 > Unit # 03: Dynamics > Newton's Laws of Motion

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Unit No. 3 Dynamics - Newton's Laws of Motion

Q. State and explain Newton’s 1st law of motion or Law of inertia with example.

Newton's First Law of Motion

Newton’s first law of motion is also known as the Law of Inertia.

Statement

"Every body continues its state of rest or of uniform motion in a straight line until it is acted upon by an external, unbalanced force to change its state of rest or uniform motion."

Explanation

This law consists of two parts:

• (a) When body is at rest: Newton's law states that when a body is at rest, it continues to remain at rest unless an external force is applied to it. Applying a force changes its state of rest and sets it into motion along a straight line.
• (b) When body is moving with uniform velocity: A body moving in a straight line with uniform velocity continues its motion unless an unbalanced opposite force acts upon it to change its state or bring it to rest.

Inertia

Inertia is the property of an object due to which it resists any change in its state of rest or uniform motion. It is essentially a measure of an object's resistance to acceleration.

Examples

• A bicycle moving along a leveled road does not come to rest immediately when pedaling stops because of its inertia of motion, until friction and air resistance gradually slow it down.
• If a bus suddenly starts moving forward, passengers standing inside fall backward. This happens because the lower part of their body in contact with the floor moves forward with the bus, while the upper part tends to remain at rest due to inertia.

Q. State and explain Newton’s 2nd law of motion and prove that $F = ma$.

Statement

"When an unbalanced force acts on an object, it produces an acceleration in the body. The acceleration is directly proportional to the applied force and inversely proportional to the mass of the object."

Explanation

If you push an object with a greater force, its velocity increases more rapidly, meaning the change in velocity takes place in the direction of the applied force. Doubling the force doubles the acceleration, assuming mass remains constant.

Derivation ($F = ma$)

According to Newton's Second Law of Motion:

• Acceleration $a$ is directly proportional to force $F$:
  $a \propto F \quad \text{--- (i)}$
• Acceleration $a$ is inversely proportional to mass $m$:
  $a \propto \frac{1}{m} \quad \text{--- (ii)}$

Combining equations (i) and (ii):

$a \propto \frac{F}{m} \quad \implies \quad a = k \frac{F}{m}$

When force ($F$), mass ($m$), and acceleration ($a$) are measured in SI units (Newtons, kilograms, and meters per second squared), the proportionality constant $k = 1$:

$a = 1 \cdot \frac{F}{m} \quad \implies \quad a = \frac{F}{m}$

$F = ma \quad \text{(Proved)}$

Q. State Newton’s 3rd law of motion with examples.

Statement

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

Explanation

When body $A$ exerts a force $F_{AB}$ on body $B$, body $B$ simultaneously exerts a force $F_{BA}$ on body $A$ that is equal in magnitude but opposite in direction:

$F_{\text{action}} = -F_{\text{reaction}} \quad \text{or} \quad F_{AB} = -F_{BA}$

The negative sign indicates that the reaction force acts in the direction opposite to the action force.

Examples

• Walking on the ground: When we walk, we push the ground backward with our feet (action), and the ground pushes us forward with an equal and opposite force (reaction), enabling us to move.
• Book on a table: A book resting on a table exerts a downward force equal to its weight on the table (action). The table exerts an equal and upward normal force on the book (reaction), keeping the book stationary.
• Rocket propulsion: When a rocket ignites its fuel, high-pressure exhaust gases are expelled downward out of the engine (action). In response, the gases exert an equal and upward reaction force on the rocket, causing it to launch and accelerate into space.

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