  # Mechanics  [ 11 Topics ]

1. #### Physical Quantities and Their Measurement 8 Videos

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 16 Videos

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 and Two Dimensions 24 Videos

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 26 Videos

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 16 Videos

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 18 Videos

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 26 Videos

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 30 Videos

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 44 Videos

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 14 Videos

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 32 Videos

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.

# Elasticity and Fluid Mechanics  [ 4 Topics ]

1. #### Elasticity 10 Videos

While studying conditions of static equilibrium under Mechanics, we conveniently assumed that the bodies under investigation remained perfectly rigid under a set of forces and torques. In reality, no solid body is perfectly rigid. So, when a system of balanced forces or couples acts on a solid body at rest, the body gets deformed. In other words, though the body does not exhibit any translational or rotational motion as a whole, different parts within it change their relative positions with respect to each other. A light wire, attached to the ceiling and holding a load at its free end, stretches in length. A book lying on a table, subjected to a tangential force on the top cover, changes in shape. A metal sphere taken to the depths of the sea shrinks in volume, albeit by a tiny fraction. The common word for any such change is deformation. The property by virtue of which a body resists any change in its size, shape or both and tends to regain its configuration on withdrawal of the deforming forces is known at the elasticity of the body. To impart in-depth knowledge on the theory of elasticity and to develop skill in solving problems based on this topic, we offer a series of video lectures titled Internal Forces and Stress, Strain, Hooke's Law and Young's Modulus, Shear Modulus, Bulk Modulus, Stress Versus Strain Graph, Elastic Potential Energy of a Deformed Body, and so on.

2. #### Fluid Statics 19 Videos

Matter can be classified into three types: solids, liquids and gases. A solid can withstand shear stress; it has definite volume and shape. Liquids and gases cannot withstand static shear stress and begin to flow under it; hence they are collectively referred to as fluids. None of the fluids has any definite shape of its own and eventually takes the shape of the vessel in which it is kept. While a liquid occupies a definite volume almost unaffected even by very high pressure, a gas can be compressed easily. Because of these distinctive features, we can tell a solid from a fluid in most cases. But there are exceptions such as asphalt. It looks so much like a solid but, in reality, it is a fluid that flows very, very slowly. A single substance may remain in any one of the three states under varying physical conditions. As you all know, if the substance is H2O, the states are named ice (solid), water (liquid) and water vapour (gas). The mechanics of fluids is governed by a number of physical principles which are based on Newton's laws of motion and other force laws. Fluid statics is that part of Fluid Mechanics which discusses fluids at rest. We shall impart a comprehensive knowledge on this topic through a series of video lectures titled Pressure at a Point, Variation of Pressure in a Static Fluid, Measurement of Pressure, Pascal's Principle, Buoyancy and Archimedes' Principle, Equilibrium of a Floating Body, and many more.

3. #### Surface Tension 2 Videos

A piece of camphor dances on the surface of water without any obvious provocation. A water spider can skate on a pond without wetting its legs. A container with a small hole at the bottom can manage to hold mercury. Great effort is required to separate two flat glass plates if there is a thin layer of water between them. When a narrow glass tube open at both ends is dipped into water, water rises in the tube. All these events can be explained by the fluid property called surface tension. Surface tension is a molecular phenomenon which occurs at the surface of separation between two phases such as a liquid and a solid, a liquid and a gas, or a solid and a gas. We shall teach you the basics of surface tension first, and then follow up with a large number of problems at both simple and challenging levels. Our video lectures on this topic are titled Theory of Surface Tension, Angle of Contact and Shape of Meniscus, Excess Pressure within Liquid Drop and Soap Bubble, Force between Two Plates Separated by a Liquid Film, Rise or Fall of a Liquid in a Capillary Tube, and much more.

4. #### Fluid Dynamics and Viscosity 3 Videos

While the motion of rigid bodies is rather uninteresting, the motion of fluids observed in nature can indeed be pleasing to the eye. The flow of a gurgling stream, the eruption of molten lava, the swirl of hot gases from a burning tinder, ocean waves – all these and more are the subject of fluid dynamics. While each particle of the fluid follows Newton's laws of motion, we find it convenient to describe the properties of the fluid at each point on its path as a function of time. The motion of a real fluid is complex and not yet fully understood. Therefore, we often make matters simple by assuming an ideal fluid which is non-viscous and incompressible. Further, the flow of the ideal fluid is assumed to be steady and irrotational. However, in the latter part of the topic, we discuss viscosity and steady flow of a viscous fluid. The students will acquire a commanding grip on the topic and will learn to solve a variety of problems – simple to moderate to difficult – through a series of video lectures titled Equation of Continuity, Bernoulli's Equation, Some Applications of Bernoulli's Equation, Viscosity, Poiseuille's Law, Critical Speed and Reynolds Number, Motion of a Solid Body in a Viscous Fluid, et cetera.

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