State and derive Newton’s laws of motion | Statement of Newton’s laws of motion | Derivation of Newton’s laws of motion | University Notes | Physics Notes | B.Sc. Physics Notes by Study Buddy Notes

Newton’s Laws of Motion

State and derive Newton’s laws of motion | Statement of Newton’s laws of motion | Derivation of Newton’s laws of motion | University Notes | Physics Notes | B.Sc. Physics Notes by Study Buddy Notes

Newton’s laws of motion describe the relationship between the forces acting on a body and its motion due to these forces. They form the foundation of classical mechanics.

1. Newton's First Law (Law of Inertia)

Statement: An object at rest remains at rest, and an object in motion continues to move with a constant velocity in a straight line, unless acted upon by an external force.

Derivation and Explanation:
This law defines inertia — the tendency of an object to resist changes in its state of motion. Mathematically, if no net force $(\sum F = 0)$ acts on a body, the velocity remains constant ($v = \text{constant}$).

Applications:

• A passenger in a moving car feels a jerk when the car suddenly stops, as their body resists the change in motion due to inertia.
• When a book lying on a table remains stationary, it is due to the absence of any unbalanced force acting on it.

---

2. Newton's Second Law (Law of Acceleration)

Statement: The rate of change of momentum of an object is directly proportional to the net external force acting on it, and this change in momentum occurs in the direction of the applied force.

Derivation and Explanation:
The second law can be mathematically represented as:

$$F = \frac{d}{dt}(mv) = m \cdot a$$

where $F$ is the force applied, $m$ is the mass of the object, and $a$ is its acceleration. This equation highlights that the force needed to accelerate an object depends on its mass and the acceleration required.

Applications:

• Pushing a heavy box requires more force than pushing a lighter one to achieve the same acceleration.
• The force applied on a ball determines how quickly it changes speed; for instance, hitting a cricket ball with a bat applies a large force, causing rapid acceleration.

---

3. Newton's Third Law (Action and Reaction)

Statement: For every action, there is an equal and opposite reaction.

Derivation and Explanation:
This law suggests that forces always occur in pairs. If object A exerts a force $F$ on object B, then object B exerts an equal and opposite force $-F$ on object A.

Applications:

• When a swimmer pushes against the wall of a pool, the wall pushes back, allowing the swimmer to move forward.
• A rocket launch illustrates this principle; the thrust of gases pushed downwards by the rocket engine creates an upward force, propelling the rocket.

---

Applications in Different Scenarios

1. Vehicle Motion and Braking:

   • First Law: Explains why a seatbelt is necessary; when a car suddenly stops, the body wants to continue moving.
   • Second Law: Calculates braking force needed to stop a car.
   • Third Law: Tires push against the ground, and the ground pushes back, moving the car forward.

2. Sports:

   • First Law: A stationary ball remains still until kicked (soccer).
   • Second Law: Hitting a baseball with a bat, where the bat exerts force on the ball to change its momentum.
   • Third Law: The force applied on the bat by the ball is equal and opposite to the force applied by the bat on the ball.

3. Space Science:

   • Third Law is fundamental in rocket propulsion, as gas is expelled downwards, creating an equal and opposite thrust force that propels the rocket upward.

4. Everyday Activities:

   • Pushing a door open involves all three laws: inertia of the door (First Law), force applied to accelerate it (Second Law), and reaction force on hand (Third Law).

---

In summary, Newton's laws provide a comprehensive framework to analyze motion and the forces involved in various natural and man-made systems.