PSY405 Handouts Lectures 1-45

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About the Handouts

The following books have been mainly followed to prepare the slides and handouts: 1. Spiegel, M.R., Theory and Problems of Vector Analysis: And an Introduction to Tensor Analysis. 1959: McGraw-Hill. 2. Spiegel, M.S., Theory and problems of theoretical mechanics. 1967: Schaum. 3. Taylor, J.R., Classical Mechanics. 2005: University Science Books. 4. DiBenedetto, E., Classical Mechanics: Theory and Mathematical Modeling. 2010: Birkhäuser Boston. 5. Fowles, G.R. and G.L. Cassiday, Analytical Mechanics. 2005: Thomson Brooks/Cole. The first two books were considered as main text books. Therefore the students are advised to read the first two books in addition to these handouts. In addition to the above mentioned books, some other reference book and material was used to get these handouts prepared. ii

Contents

Module No. 79.............................................................................................................................................. 1

Module No. 80.............................................................................................................................................. 2

Module No. 81.............................................................................................................................................. 4 Introductions to Rectangular Components of Velocity & Acceleration ............................................ 4 Module No. 82.............................................................................................................................................. 6 Introduction to Tangential and Normal Components of Velocity & Acceleration ........................... 6 Module No. 83.............................................................................................................................................. 8 Example of Tangential and Normal Acceleration ................................................................................ 8 Module No. 84............................................................................................................................................ 10 Curvature and Radius of Curvature ................................................................................................... 10 Module No. 85............................................................................................................................................ 12 Introduction to Radial and Transverse Components of Velocity & Acceleration .......................... 12 Module No. 86............................................................................................................................................ 14 Example of Radial and Transverse Components of Velocity and Acceleration .............................. 14 Module No. 87............................................................................................................................................ 15 Reference System or Inertial Frame ................................................................................................... 15 Module No. 88............................................................................................................................................ 16 Example of inertial Frame ................................................................................................................... 16 Module No. 89............................................................................................................................................ 18 Newton's First and Second Laws ......................................................................................................... 18 Module No. 90............................................................................................................................................ 20 The Third Law and Law of Conservation of Momentum ................................................................. 20 Module No. 91............................................................................................................................................ 23 Validity of Newton’s Law ..................................................................................................................... 23 Module No. 92............................................................................................................................................ 24 Example of Newton’s Law 1, 2 ............................................................................................................. 24 Module No. 93............................................................................................................................................ 27 Example of Newton’s Law: 3 ............................................................................................................... 27 Module No. 94............................................................................................................................................ 29 Introduction to Energy: Kinetic Energy ............................................................................................. 29

Module No. 79

Mechanics is the science of motion. It studies the states of rest and motion and the laws governing rest, equilibrium and motion. A broad division of mechanics is made through the terms classical mechanics and quantum mechanics.

Classical Mechanics

The science of classical mechanics deals with the motion of objects through absolute space and time in the Newtonian sense. Classical mechanics deals with the macroscopic object i.e. those bodies which we encounter in everyday life. Such bodies may be those bodies in the form of billiard balls, parts of machinery and astronomical bodies. Classical mechanics itself has two broad divisions in the form of non-relativistic and relativistic mechanics. Non-relativistic mechanics, based on the laws of Newton is concerned with bodies moving at speeds and velocity negligibly small as compared to the speed of light 𝑐= 3 × 105per kilometer per second. Relativistic mechanics is dispensable for particles and

bodies moving with speed comparable to the speed of light.

Quantum mechanics

The quantum mechanics is the mechanics of microscopic object. Its basic concepts, principals and laws are of entirely different from those of classical mechanics.

Division of Classical Mechanics

Three major divisions of classical mechanics are the following: Mechanics of particles and rigid bodies: It is based on newton’s law. Basic concepts and terms are space, time and mass; particle and body; velocity, momentum and acceleration; force and energy. Mechanics of fluid: it is also based on newton’s law and their extensions and deal with the behavior of the fluid (liquid and gases) in motion. Its two well-known branches are hydrodynamics (for fluid) and Aerodynamics (for gases).