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Engineering Mechanics

Engineering Mechanics

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Introduction to Vectors

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Introduction to Vectors

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Engineering Mechanics

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  1. 1 Introduction to Vectors
  2. 2 Addition and subtraction of vectors
  3. 3 Multiplying vectors
  4. 4 Introduction to vectors: solved examples I
  5. 5 Transformation of vectors under rotation
  6. 6 Vector products and their geometric interpretation
  7. 7 Vector Product: Kronecker Delta and Levi-Civita symbols-I
  8. 8 Vector Product: Kronecker Delta and Levi-Civita symbols-II
  9. 9 Introduction to vectors: solved examples II
  10. 10 Equilibrium of rigid bodies – Forces and torques
  11. 11 Calculating torques and couple moments - I
  12. 12 Calculating torques and couple moments - II
  13. 13 Finding a force and a couple equivalent to an applied force
  14. 14 Different elements and associated forces and torques - I
  15. 15 Different elements and associated forces and torques - II
  16. 16 Solved examples; equilibrium of bodies – I
  17. 17 Solved examples; equilibrium of bodies – II
  18. 18 Forces in different geometric configurations
  19. 19 Plane trusses I - Building a truss and condition for it to be statically determinate
  20. 20 Plane trusses II - Calculating forces in a simple truss and different types of trusses
  21. 21 Plane trusses III - Calculating forces in a simple truss by method of joints
  22. 22 Plane trusses IV - Solved examples for calculating forces in a simple truss by method of joints
  23. 23 Plane trusses V - Solved examples for calculating forces in a simple truss by method of joints
  24. 24 Plane trusses VI: Method of sections for calculating forces in a simple truss
  25. 25 Dry friction I - introduction with an example
  26. 26 Dry friction II - a solved example
  27. 27 Dry friction III - Dry thrust bearing and belt friction with demonstration
  28. 28 Dry friction IV - Screw friction and rolling friction
  29. 29 Dry friction V: Solved examples
  30. 30 Properties of plane surfaces I - First moment and centroid of an area
  31. 31 Properties of plane surfaces II - Centroid of an area made by joining several plane surfaces
  32. 32 Properties of plane surfaces III - Centroid of a distributed force and its relation with centre...
  33. 33 Properties of plane surfaces IV - solved examples of calculation of first moment and centroid...
  34. 34 Properties of plane surfaces V- Second moment and product of an area and radius of gyration
  35. 35 Properties of plane surfaces VI - Parallel axis transfer theorem for second moment and product of an
  36. 36 Properties of plane surfaces VII - transformation of second moment and product of an area under rota
  37. 37 Properties of plane surfaces VIII - second moment and product of an area, solved examples
  38. 38 Method of virtual work I - degrees of freedom, constraints and constraint forces
  39. 39 Method of virtual work II - virtual displacement, virtual work and equilibrium condition in terms of
  40. 40 Method of virtual work III - solved examples
  41. 41 Motion of a particle in a plane in terms of planar polar coordinates
  42. 42 Planar polar coordinates: solved examples
  43. 43 Description of motion in cylindrical and spherical coordinate systems
  44. 44 Using planar polar, cylindrical and spherical coordinate systems: solved examples
  45. 45 Motion with constraints, constraint forces and free body diagram
  46. 46 Motion with constraints – solved examples
  47. 47 Motion with dry friction – solved examples
  48. 48 Motion with drag – solved examples
  49. 49 Equation of motion in terms of linear momentum and the principle of conservation of linear momentum
  50. 50 Linear momentum and centre of mass
  51. 51 Momentum transfer, impulse and force due to a stream of particles hitting an object
  52. 52 Momentum and the variable mass problem
  53. 53 Linear momentum – solved examples
  54. 54 Work and energy I - work energy theorem; conservative and non-conservative force fields
  55. 55 Work and energy II - Definition of potential energy for conservative forces; total mechanical energy
  56. 56 Work and energy III - Two solved examples using conservation principles
  57. 57 Work and energy IV – Further discussion on potential energy
  58. 58 Work and energy V - Solved examples
  59. 59 Work and energy VI – Applying conservation principles to solve a collision problem
  60. 60 Work and energy VII - Solved examples
  61. 61 Rigid body motion I - degrees of freedom and number of variables required to describe motion of a ri
  62. 62 Rigid body motion II - Equation of motion for a single particle in terms of angular momentum and tor
  63. 63 Rigid body motion III - Conservation of angular momentum; angular momentum for a collection of parti
  64. 64 Rigid body motion IV - applying angular momentum conservation, a solved example
  65. 65 Rigid body motion V (fixed axis rotation) - some demonstrations of conservation of angular momentum
  66. 66 Rigid body motion VI (fixed axis rotation) - Some more demonstrations and related problems
  67. 67 Rigid body motion VII (fixed axis rotation) - Kinetic energy and moment of inertia for fixed axis ro
  68. 68 Rigid body motion VIII (fixed axis rotation) - solved examples for calculating moment of inertia and
  69. 69 Rigid body motion –IX (fixed axis rotation): solved examples
  70. 70 Rigid body motion X - rotation and translation with axis moving parallel to itself
  71. 71 Rigid body motion XI - solved examples for rotation and translation with axis moving parallel to its
  72. 72 Rigid-body dynamics XII - Some demonstrations on general motion of rigid bodies
  73. 73 Rigid-body dynamics XIII - Infinitesimal angles as vector quantities and change of a vector when rot
  74. 74 Rigid-body dynamics XIV - Angular velocity and the rate of change of a rotating vector; relating cha
  75. 75 Rigid-body dynamics XV - Relationship between angular momentum and angular velocity – the moment of
  76. 76 Rigid-body dynamics XVI: Solved examples
  77. 77 Rigid body motion XVII – A review of the relation between angular momentum and angular velocity, mom
  78. 78 Rigid body motion XVIII- Solved examples for calculating rate of change of angular momentum and torq
  79. 79 Rigid body dynamics XIX: understanding demonstrations shown earlier using equation of motion
  80. 80 Rigid body dynamics XX - understanding demonstrations shown earlier using equation of motion (Euler
  81. 81 Rigid body dynamics XXI - Euler equations, solved examples
  82. 82 Simple harmonic motion I - expanding potential energy about the equilibrium point and the correspond
  83. 83 Simple harmonic motion II : solving the equation of motion with given initial conditions
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