### Potential Analysis & introduction of Equation of Motion Lecture 3

Course Overview CSIR NET Physical Science Online Live Class proceeds from an explanation of theory to problem solving, helping you build a strong knowledge

### Potential Analysis

Potential analysis is a crucial concept in classical mechanics, offering a method to understand forces and the resulting motions of objects. The potential energy of a system represents the stored energy due to the position of objects within a force field, such as gravitational or electrostatic fields. The key idea is that the work done by conservative forces can be described in terms of changes in potential energy.

#### Gravitational Potential Energy

For an object of mass m near the Earth’s surface, the gravitational potential energy is given by: Ug=mgh

where:

- Ug is the gravitational potential energy,
- m is the mass of the object,
- g is the acceleration due to gravity,
- h is the height above a reference level.

Elastic Potential Energy, Electrostatic Potential Energy,

### Introduction to Equations of Motion

The equations of motion are fundamental tools in classical mechanics that describe the relationship between an object’s position, velocity, and acceleration over time. They provide a mathematical framework for analyzing the motion of objects under the influence of forces.

#### Newton’s First Law (Law of Inertia)

An object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.

#### Newton’s Second Law (Law of Acceleration)

The rate of change of momentum of an object is directly proportional to the net force acting on it and occurs in the direction of the net force. F=ma

where:

- F is the net force,
- m is the mass of the object,
- a is the acceleration.

#### Newton’s Third Law (Action and Reaction)

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

#### Equations of Motion for Uniform Acceleration

These equations apply to objects moving with constant acceleration:

These equations form the basis for solving a wide range of problems in mechanics, from the motion of projectiles to the dynamics of planetary orbits. Understanding and applying these principles is essential for success in exams like the CSIR NET/JRF Physics.