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Mechanics

1. PHYSICAL QUANTITIES AND THEIR MEASUREMENT

The analysis of physical phenomena and processes requires the measurement of physical quantities. A physical quantity is measured in terms of a small part of it. The small part is conventionally adopted as a unit of measurement of the quantity. We can choose such a unit for every quantity independent of other quantities. However, it is helpful to first establish the units of a few quantities which are called base or fundamental quantities. The corresponding units are called base or fundamental units. The units of the remaining physical quantities are expressed in terms of these base units. These quantities are called derived quantities and their units, derived units. To firm up your basic knowledge we have videos on Base and Derived Quantities and Their Units, Principle of Homogeneity of Dimensions, Order of Magnitude Calculation, Uses of Dimensional Analysis etc.


2. VECTORS

A quantity which is completely specified by a number with an appropriate unit is called a scalar. A scalar has only magnitude but no direction. Some scalars like volume and mass are always positive. Other scalars like temperature and electric charge can be either positive or negative. A quantity which is completely specified by a number with an appropriate unit and direction is called a vector. Thus, a vector has both magnitude and direction. Examples of vectors are velocity, acceleration, force, momentum, torque etc. We have video lectures on Addition of Vectors, Subtraction of Vectors, Resolution of Vectors, Product of Vectors and other aspects of vector with suitable examples and problems.


3. MOTION IN ONE OR TWO DIMENSIONS

Mechanics can be divided into two parts: dynamics and statics. Dynamics is the study of motion of a body under one or more forces. Statics is the study of the condition of rest of a body under a number of forces. Dynamics is further divided into kinematics and kinetics. Kinematics is that part of dynamics which deals with motion without reference to the forces that cause it or the properties of the body in motion. Kinetics is that part which relates the motion of a body to its mass and the casual force(s). The subtopics covered in the present topic such as Projectile Motion, Translational Motion, Graphical Analysis of Rectilinear Motion, Rectilinear Motion with Constant Acceleration, Rectilinear Motion under Gravity etc. fall within the scope of kinematics.


4. NEWTON’S LAWS OF MOTION

Newton’s three laws of motion are fundamental to the study of Kinetics. Kinetics is the study of how motion of a body is related to its mass and the force(s) acting on it. The force represents the interaction of a body with its environment. In general, the environment consists of nearby bodies and the effect of distant bodies may be ignored. The mass of a body is a measure of its inertia which is the tendency to resist acceleration under a force. The theory of motion was developed by English physicist Sir Isaac Newton (1642 – 1727) in the 17th century. We have video lectures on various subtopics such as Newton’s Laws of Motion, Concept of Force, Free Body Diagrams, Applications of Newton’s Laws, Pseudo Force, Comparison of Inertial Frame And Non-Inertial Frame etc. to provide an in-depth knowledge in an extremely skillful way.


5. FRICTION

We often simplify problems by assuming that the motion of bodies takes place on “frictionless” surfaces. Strictly speaking, there is no such surface. In real life all motions happening around us are affected by the force of friction. Therefore, a realistic approach to any mechanical problem requires that we identify the frictional forces acting on the system and include them in the respective equations of motion. That is precisely what you will learn to do in the present topic. You will find video lectures on Static and Kinetic friction, Angle of Repose, Angle of Friction, Examples of Motion on Rough Surfaces, Rolling Friction, Drag Force etc. explained and supported by suitable applications and numerical examples.


6. CIRCULAR MOTION

In the present topic, the same motion will be discussed in greater detail. The topic deals with the kinematics of circular motion without any reference to the forces that cause it as well as the contribution of the forces acting on a particle, causing its circular motion. The study of circular motion is not only important in itself, but also an essential precondition for the study of rotational motion. When a rigid body rotates about an axis, every particle of it describes a circle whose centre lies on the axis of rotation. Therefore, the kinematic equations that we develop in this topic will also be useful to study rotational motion. This topic consists of video lectures on Angular Quantities in Circular Motion, Circular Motion with Constant Angular Acceleration, Two Accelerations of Non-Uniform Circular Motion, Problems on Circular Motion and many more to provide a thorough knowledge and to guide students to develop the problem-solving skill.


7. WORK AND ENERGY

Until now we used terms like velocity, acceleration, force etc. which mean more or less the same thing to a physicist and a layman. The term work is an exception. In ordinary conversation the word may mean a wide variety of activities, but in the domain of physics, its use is far more restricted. The concept of energy is closely associated with that of work. Be it a physicist or a common man, everyone has an awareness of energy and what it truly means. We shall mostly be dealing with Mechanical Energy which is further classified into two types: Kinetic Energy and Potential Energy. Through our video lectures on Definition of Work, Work Done by a Varying Force, Concept of Energy and Derivation of Work-Energy theorem, Principle of Conservation of Mechanical energy and Some Applications, Equivalence of Mass and energy, Conservative and Non-Conservative Forces, Potential Energy Function, Principle of Conservation of Mechanical Energy and Some Applications etc. we elaborately illustrated the topic for a crystal clear understanding and application.


8. IMPULSE, COLLISION, AND CENTRE OF MASS

As the title suggests, this topic can be broadly divided into three sections. In this topic we have defined impulse of a force, the impulse-momentum theorem, the principle of conservation of linear momentum etc. You have already been introduced to the concept of momentum in the topic 4 (Newton’s Laws of Motion). But it needs more than that brief introduction to have a stronger grasp on the topic. The most useful application of the momentum principle is the study of collision between two bodies. The definition of the centre of mass of a system of particle will show the motion of a system of particles is equivalent to the motion of one representative particle located at the centre of mass. You will develop a clear concept of the topic through the video lectures on Impulse and Impulse-Momentum Theorem, Motion of a Body of Variable Mass, Principle of Conservation of Linear Momentum, Collision in One Dimension, Collision in Two Dimensions, Finding Centres of Mass of Uniform Rigid Bodies, Motion of a System of Particles etc.


9. ROTATIONAL MECHANICS

When a rigid body performs rotational motion, the individual particles follow different paths and process, different linear velocities and accelerations at any particular instant. The study of rotational motion in the present topic requires that we treat the body as an assemblage of many particles, connected firmly to one another and each moving with its own velocity and acceleration. To strengthen your concept and consolidate your problem-solving skill we offer you video lectures on Kinematics of Rotation about a Fixed Axis, Equation of Rotational Motion of Rigid Body, Torque of a Force Acting on a Particle, Two Important Theorem on Moment of Inertia, Equation of Rotational Motion of a Rigid Body, Over Turning of Vehicles at a Bend, Angular momentum of a Particle and Its Relation with Torque and many more.


10. STATICS OF RIGID BODIES

When engineers construct buildings and flyovers and designers design small items like scissors, forks, ect, they keep two things in mind. First, the conditions under which the bodies, presumed to be rigid, remain in mechanical equilibrium under the action of external forces and their torques. And second, the conditions under which the bodies continue to remain rigid under the said forces and torques.The branch of physics which studies the condition of equilibrium of a body at rest is called statics. All bodies which attain equilibrium under a set of forces are deformed to a certain extent. However, if these forces are comparatively small, the deformation is also small and the conditions of static equilibrium remain unaffected. At this point, it will be tacitly assumed that the bodies under investigation remain perfectly rigid when a set of forces and torques act on them. You will enjoy the topic while learning through the video lectures on Stability of Static Equilibrium, Various Cases of Static Equilibrium In Two Dimensions, Equilibrium of A Leaning Ladder, Centre of Gravity of a Rigid Body and many more.


11. GRAVITATION

We told you in topic 4 that the gravitational force is one of the three fundamental forces of nature, the other two being the electromagnetic force and the nuclear force. The nuclear force operates inside an atomic nucleus and does not make its presence felt in everyday life. The electromagnetic force is often disguised as various forms of contact force. But whether it is the orbital motion of a planet round the sun or the free fall of an apple from a tree, the effect of the gravitational force is easy for all to feel. For your easy understanding of the subject and to increase your level of command to crack and solve the variety of numerical problems, we have video lectures on Newton’s Law of Universal Gravitation, Determination of the Gravitational Constant G, Kepler’s Laws of Planetary Motion, Gravity, Gravitational Field, Gravitational Potential Energy, Gravitational Potential, Escape Speed, Natural and Artificial Satellites of Motion, Mechanical Energy of Satellite-Earth System, etc.


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