Course Overview
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Course Synopsis
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Test
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Course Learning Outcomes
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Learning Outcomes Vectors and Classical Mechanics
- Differentiate between scalar and vector field and understand the role of gradient divergence curl.
- Apply the fundamental theorems of vector calculus such as the divergence theorem and Stokes39 theorem to solve practical problems in physics and engineering.
- Demonstrate competence in computing line integrals surface integrals and volume integrals in different coordinate systems.
- Demonstrate proficiency in analyzing the Newton laws of motion of particles and rigid bodies in both rectilinear and curvilinear coordinates.
- Understand the concept of rotational motion and be able to compute key parameters such as moment of inertia and angular momentum for various geometric shapes.
- Apply the principles of work energy and power to solve problems involving mechanical systems. analyze motion relative to different frames of reference including inertial and rotating frames. Also applying equations of motion in rotating frames of reference for solving realworld problems.
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Course Calendar
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Week 01
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1
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Introduction of the Course
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2
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Scalar and Vector Fields
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3
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The operator Del and Gradient of function
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4
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Properties of the Gradient
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6
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Theorem related to Directional Derivative
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7
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Example of Directional Derivative
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8
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Problem related to Directional Derivative
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9
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Problem 2 related to Directional Derivative
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10
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Problem 3 related to Directional Derivative
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11
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Geometrical interpretation of Gradient
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12
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Gradient related Theorem
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13
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Gradient related Problem 1
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14
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Gradient related Problem 2
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15
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Gradient related Problem 3
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Week 02
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16
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Divergence of a vector Point Function
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17
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Properties of the Divergence
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20
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Problem 1 Related to Divergence
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21
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Problem 2 Related to Divergence
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22
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Problem 3 Related to Divergence
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23
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Curl of a vector Point Function
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24
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Properties of the Curl
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26
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Problem 1 related to Curl
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27
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Problem 2 related to Curl
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28
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Problem 3 related to Curl
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Week 03
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31
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Other forms and general properties of line integrals
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32
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Example of Line Integral
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33
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Example 2 of Line Integral
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34
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Line Integral dependent on Path
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35
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Line Integral Independent of Path
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36
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Theorems on line integral
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37
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Problem 1 on Line Integral
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38
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Problem 2 on Line Integral
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39
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Problem 3 on Line Integral
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40
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Problem 4 on Line Integral
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Week 04
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42
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Evaluation of the surface integral
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43
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Example of surface integral
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44
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Example 2 of surface integral
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45
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Problem 1 of surface integral
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46
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Problem 2 of surface integral
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47
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Problem 3 of surface integral
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Assignment 1
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49
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Example 1 of Volume integral
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50
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Problem 1 of Volume integral
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51
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Problem 2 of Volume integral
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Week 05
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53
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Divergence theorem in Rectangular Form
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54
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Verification of Divergence theorem by an Example
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55
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Verification of Divergence theorem by Example 2
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56
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Example 1 of Divergence theorem
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57
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Example 2 of Divergence theorem
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58
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Example 3 of Divergence theorem
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60
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Stokes’ theorem in Rectangular Form
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61
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Verification of Stokes’ theorem by Example 1
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62
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Verification of Stokes’ theorem by Example 2
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63
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Theorem related to Stokes’ theorem
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64
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Example 1 of Stokes’ Theorem
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65
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Example 2 of Stokes’ Theorem
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66
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Example 3 of Stokes’ Theorem
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Quiz 1
Week 06
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67
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Simply and Multiply Connected Regions
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68
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Green’s Theorem in the Plane
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69
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Example of Green’s Theorem in the Plane
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70
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Green's theorem in the plane in vector notation
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71
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Green's theorem in the plane as special case of Stokes' theorem
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72
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Gauss' divergence theorem as generalization of Green's theorem
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73
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Green’s first identity
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74
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Green’s second identity
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75
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Example of Green's Identity
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76
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Problem 1 of Green's Identity
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77
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Problem 2 of Green's Identity
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78
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Problem 3 of Green's Identity
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Week 07
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79
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Introduction to Classical Mechanics
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80
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Introduction to the basics of newton’s law
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81
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Introduction to Rectangular components of velocity & acceleration
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82
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Introduction to tangential and normal components of velocity & acceleration
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83
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Example of tangential and normal acceleration
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84
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Curvature and radius of curvature with example
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85
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Introduction to radial an transverse components of velocity & acceleration
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86
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Example of radial velocity and acceleration
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87
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Inertial reference system and inertial frame
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Quiz 2
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89
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Newton's first and second laws
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90
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The third law and law of Conservation of momentum
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91
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Validity of Newton’s law
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92
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Example of newton’s first and second law
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93
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Example of newton’s third law
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Week 08
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94
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Introduction to energy : Kinetic energy
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95
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Introduction to work - Theorem
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Mid Term Examination
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97
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Conservative force field
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98
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Example of conservative field
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99
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Related Topic of conservative force fields
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100
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Non-conservative Force field
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101
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Example of non- conservative field
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Week 09
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102
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Introduction to simple harmonic motion and Oscillator
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103
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Amplitude , time period, frequency and energy of Simple Harmonic Motion
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104
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Example of Simple Harmonic Motion
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105
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Example of energy of Simple Harmonic Motion
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106
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Introduction to damped harmonic oscillator
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107
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Example of Damped Harmonic Oscillator
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108
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Euler’s theorem - derivation
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110
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Kinematics of a system of particles(space, time & matter)
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111
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The concept of Rectilinear motion of particles Uniform rectilinear motion, uniformly accelerated rectilinear motion
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112
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The concept of curvilinear motion of particles
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113
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Example related to curvilinear coordinates
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114
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Introduction to Projectile, motion of a projectile
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115
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Conservation of energy for a system of particles
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116
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Examples of Conservation of energy for a system of particles
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Week 10
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117
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Introduction to impulse - Derivation
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119
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Introduction to torque
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121
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Introduction to Rigid Bodies and Elastic Bodies
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122
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Properties of Rigid Bodies
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123
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Instantaneous Axis and Center of Rotation
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124
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Centre of Mass, Motion of the Center of Mass
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125
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Definition of Moment of Inertia and Product of Inertia
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126
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Example of Moment of Inertia and Product of Inertia
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127
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Radius of Gyration with Example
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128
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Principal Axes for the Inertia Matrix
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Week 11
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129
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Introduction to the Dynamics of a System of Particles
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130
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Introduction to Center of Mass and Linear Momentum
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Quiz 3
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131
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Law of Conservation of Momentum for Multiple Particles
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132
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Example of Conservation of Momentum
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133
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Angular Momentum – Derivation
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134
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Angular Momentum in Case of Continuous Distribution of Mass
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135
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Law of Conservation of Angular Momentum
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136
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Example of Angular Momentum
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137
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Kinetic Energy of a System about Principal Axes – Derivation
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138
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Moment of Inertia of a Rigid Body about a given Line
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139
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Example of Moment of Inertia of a rigid body about given line
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141
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Rotational Kinetic Energy
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Week 12
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142
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Moment of Inertia & Angular Momentum in Tensor Notation
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143
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Introduction to Special Moments of Inertia
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144
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Moment of Inertia of the Thin Rod – Derivation
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145
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Moment of Inertia of Hoop or Circular Ring – Derivation
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146
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Moment of Inertia of Annular Disk - Derivation
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147
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Moment of Inertia of a Circular Disk - Derivation
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148
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Rectangular Plate – Derivation
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149
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Moment of Inertia of Square Plate – Derivation
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150
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Moment of Inertia of Triangular Lamina – Derivation
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151
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Moment of Inertia of Elliptical Plate along its Major Axis – Derivation
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152
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Moment of Inertia of a Solid Circular Cylinder - Derivation
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153
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Moment of Inertia of Hollow Cylindrical Shell - Derivation
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Week 13
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154
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Moment of Inertia of Solid Sphere - Derivation
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155
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Moment of Inertia of the Hollow Sphere – Derivation
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156
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Inertia Matrix / Tensor of solid Cuboid
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157
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Problem related to Inertia Matrix / Tensor of solid Cuboid
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158
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Moment of Inertia of Hemi-Sphere – Derivation
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Quiz 4
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159
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Moment of Inertia of Ellipsoid –Derivation
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160
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Example 1 of Moment of Inertia
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161
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Example 2 of Moment of Inertia
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162
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Example 3 of Moment of Inertia
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163
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Example 4 of Moment of Inertia
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164
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Example 5 of Moment of Inertia
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165
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Theorem on Moment of Inertia
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Week 14
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166
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Example 1 of Parallel Axis Theorem
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167
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Example 2 of Parallel Axis Theorem
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168
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Example 3 of Parallel Axis Theorem
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169
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Example 4 of Parallel Axis Theorem
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170
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Perpendicular Axis Theorem
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171
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Example 1 of Perpendicular Axis Theorem
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172
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Example 2 of Perpendicular Axis Theorem
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173
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Example 3 of Perpendicular Axis Theorem
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174
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Problem of Moment of Inertia
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175
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Existence of Principle Axes
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176
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Determination of Principal Axes of Other Two When One is known
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177
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Determination of Principal Axes by Diagonalizing the Inertia Matrix
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Week 15
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178
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Relation of Fixed and Rotating Frames of Reference
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179
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Equation of Motion in Rotating Frame of Reference
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180
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Example 1 of Equation of Motion in Rotating Frame of Reference
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181
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Example 2 of Equation of Motion in Rotating Frame of Reference
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182
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Example 3 of Equation of Motion in Rotating Frame of Reference
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183
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Example 4 of Equation of Motion in Rotating Frame of Reference
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184
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Example 5 of Equation of Motion in Rotating Frame of Reference
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185
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General Motion of a Rigid Body
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186
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Equation of Motion Relative to Coordinate System Fixed on Earth
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Final Term Examination
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