UPSC Physics Optional Notes (Paper I) 2023

Sample Chapter

Laws of motion

The laws of motion are a set of fundamental principles formulated by Sir Isaac Newton in the 17th century. These laws describe the motion of objects and the forces acting upon them. The laws of motion laid the foundation for classical mechanics and are still widely used in physics to understand the behavior of objects in motion. There are three laws of motion:

1. Newton’s First Law of Motion (Law of Inertia): This law states that an object at rest will remain at rest, and an object in motion will continue to move with a constant velocity along a straight line, unless acted upon by an external force. In other words, an object will maintain its state of motion unless a force is applied to it.
2. Newton’s Second Law of Motion (Law of Acceleration): This law states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. Mathematically, it can be expressed as F = ma, where F is the net force acting on an object, m is its mass, and a is the acceleration produced.
3. Newton’s Third Law of Motion (Law of Action and Reaction): This law states that for every action, there is an equal and opposite reaction. When an object exerts a force on another object, the second object exerts an equal and opposite force on the first object. The forces always occur in pairs and act on different objects.

These laws provide a framework for understanding and predicting the motion of objects under the influence of forces. They have applications in various fields, including engineering, physics, and everyday life, and are essential for studying mechanics, dynamics, and kinematics.

Conservation of Energy and Momentum

Law of conservation of Energy

The law of conservation of energy states that energy cannot be created or destroyed, but it can only be transferred or transformed from one form to another. In a closed system where no external forces are acting, the total energy remains constant. This principle is derived from the fundamental nature of energy and is applicable to various physical phenomena.

According to the conservation of energy, the total energy of a system remains constant, even if it changes from one form to another. Energy can exist in various forms, such as kinetic energy (energy of motion), potential energy (energy due to position or configuration), thermal energy (energy associated with temperature), electrical energy, chemical energy, and so on. The total energy of a system is the sum of all these forms.

For example, if an object is dropped from a certain height, its potential energy decreases as it falls, but its kinetic energy increases. The total energy of the system (object plus Earth) remains constant throughout the process, neglecting any dissipative forces like air resistance.

Conservation of Momentum

The law of conservation of momentum states that the total momentum of a closed system remains constant if no external forces act on it. Momentum is defined as the product of an object’s mass and velocity. Mathematically, momentum (p) is expressed as p = mv, where m is the mass of the object and v is its velocity.

When two or more objects interact within a closed system, the total momentum before the interaction is equal to the total momentum after the interaction, provided there are no external forces acting. This principle is derived from Newton’s third law of motion (action and reaction).

For example, in a collision between two objects, the total momentum of the system before the collision is equal to the total momentum after the collision. If one object gains momentum, the other object will experience an equal and opposite change in momentum to maintain the conservation principle.

Conservation of momentum is widely used in various fields, such as physics, engineering, and astronomy, to analyze and predict the behavior of objects in motion. It is particularly valuable in studying collisions, explosions, and other interactions between objects.