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Applications of Calculus to Mechanics

Applications of Calculus to Mechanics

Eddie Woo via YouTube Direct link

Full Derivation of Acceleration = d(½v²)/dx

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Full Derivation of Acceleration = d(½v²)/dx

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Applications of Calculus to Mechanics

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  1. 1 Functions of Displacement: Example Question
  2. 2 Functions of Displacement: Harder Example (1 of 3 - Finding v²)
  3. 3 Functions of Displacement: Prologue
  4. 4 Functions of Displacement: Proof 1
  5. 5 Functions of Displacement: Proof 2
  6. 6 Functions of Displacement: Harder Example (2 of 3 - Integrating for x)
  7. 7 Functions of Displacement: Harder Example (3 of 3 - Establishing Domain for v)
  8. 8 Gravity & Escape Velocity (1 of 3)
  9. 9 Gravity & Escape Velocity (2 of 3)
  10. 10 Gravity & Escape Velocity (3 of 3)
  11. 11 Introduction to Simple Harmonic Motion
  12. 12 Simple Harmonic Motion: Basic Equations
  13. 13 Characteristics of Simple Harmonic Motion (1 of 2)
  14. 14 Characteristics of Simple Harmonic Motion (2 of 2)
  15. 15 Simple Harmonic Motion: Amplitude Example
  16. 16 Simple Harmonic Motion: Shifted Centre Example (1 of 2)
  17. 17 Simple Harmonic Motion: Shifting the Centre
  18. 18 Simple Harmonic Motion: Shifted Centre Example (2 of 2)
  19. 19 Projectile Motion: North Korean Tank (1 of 4)
  20. 20 Projectile Motion: North Korean Tank (2 of 4)
  21. 21 Projectile Motion: North Korean Tank (3 of 4)
  22. 22 Projectile Motion: Summary of Equations
  23. 23 Projectile Motion: Glenn Mcgrath (1 of 2)
  24. 24 Projectile Motion: Glenn Mcgrath (2 of 2)
  25. 25 Projectile Motion: North Korean Tank (4 of 4)
  26. 26 Projectile Motion: Colliding Particles (1 of 3)
  27. 27 Projectile Motion: Colliding Particles (2 of 3)
  28. 28 Projectile Motion: Colliding Particles (3 of 3)
  29. 29 Tricky Projectile Question: Different Angles of Projection
  30. 30 Tricky Projectile Question: Equation of Path
  31. 31 Tricky Projectile Question: Restriction on Angles
  32. 32 Interpreting Displacement-Time Graphs
  33. 33 Integrating Motion Equations: The Tennis Ball (1 of 3)
  34. 34 Integrating Motion Equations: The Tennis Ball (2 of 3)
  35. 35 Integrating Motion Equations: The Tennis Ball (3 of 3)
  36. 36 Introduction to Simple Harmonic Motion: Time Equations
  37. 37 Key Illustration for Understanding Simple Harmonic Motion
  38. 38 Physical Models and their Differential Equations
  39. 39 Simple Harmonic Motion Example Question: The Spring
  40. 40 Understanding SHM by examining its graphs
  41. 41 Introductory Guide to Describing Motion
  42. 42 Velocity as a Function of Displacement
  43. 43 Acceleration in terms of Velocity (1 of 2: Review)
  44. 44 Acceleration in terms of Velocity (2 of 2: Derivation & Example)
  45. 45 The Ball & Stone (1 of 2: Finding Time of Collision)
  46. 46 The Ball & Stone (2 of 2: Determining Restriction on V)
  47. 47 Simple Harmonic Not-Motion: Fluctuating Temperature
  48. 48 Projectile Motion: Simple Worked Example (1 of 4: Resolving Initial Velocity)
  49. 49 Projectile Motion: Simple Worked Example (2 of 4: Developing 4 Time Equations)
  50. 50 Projectile Motion: Simple Worked Example (3 of 4: Understanding the Point of Impact)
  51. 51 Projectile Motion: Simple Worked Example (4 of 4: Equation of Path)
  52. 52 Projectile Motion: Aiming for a Target (1 of 2: Generating Time Equations)
  53. 53 Projectile Motion: Aiming for a Target (2 of 2: Determining Firing Angle)
  54. 54 Relationship Between High & Low Firing Angles
  55. 55 Equation of Path Example Question (1 of 2): Identifying Important Features
  56. 56 Equation of Path Example Question (2 of 2): Adding in a Slanted Road
  57. 57 Equation of Path: Understanding Time as the Parameter
  58. 58 Mid-Air Target Question (1 of 4): Time of Equal Horizontal/Vertical Displacement
  59. 59 Mid-Air Target Question (2 of 4): Time of Impact
  60. 60 Mid-Air Target Question (3 of 4): Implied Restriction on Firing Angle
  61. 61 Mid-Air Target Question (4 of 4): Two Final Results
  62. 62 Exam Problem: Simple Harmonic Motion with Auxiliary Angle
  63. 63 Defining Momentum & Force
  64. 64 Introduction to Mechanics
  65. 65 Newton's First Law: Inertia
  66. 66 Mechanics Example 1: Using F = ma to find v(t)
  67. 67 Newton's Second Law: Inertial Mass
  68. 68 Newton's Third Law: Reactions
  69. 69 Mechanics Example 2: Using F = ma to find v(x)
  70. 70 Mechanics Example 3: Starting from Displacement Function
  71. 71 Mechanics Example 4: Calculating Total Distance of a Multi-Step Journey
  72. 72 Weight
  73. 73 Introduction to Resisted Motion (1 of 2: What is Resistance?)
  74. 74 Introduction to Resisted Motion (2 of 2: Example question)
  75. 75 Resistance - should it be kv or mkv? (1 of 3: Introductory thoughts)
  76. 76 Resistance - should it be kv or mkv? (2 of 3: Inferring from details in the question)
  77. 77 Resistance - should it be kv or mkv? (3 of 3: What to do when it's ambiguous)
  78. 78 Vertical Resistance & Gravity example question (1 of 2: Finding x(v))
  79. 79 Vertical Resistance & Gravity example question (2 of 2: Proving Final Result)
  80. 80 Vertical Resistance & Gravity: Framing the Question
  81. 81 Mechanics Example 5: Momentum, Terminal Velocity & Total Distance
  82. 82 Physics vs. "Motion" in Mathematics (1 of 2: What's included?)
  83. 83 Physics vs. "Motion" in Mathematics (2 of 2: What's different?)
  84. 84 Types of Motion in HSC Mathematics (2U, Ext 1 & Ext 2)
  85. 85 Introduction to Simple Harmonic Motion (1 of 2: Key Features)
  86. 86 Introduction to Simple Harmonic Motion (2 of 2: Time Equations)
  87. 87 Simple Harmonic Motion Question (1 of 3: Basic Features)
  88. 88 Simple Harmonic Motion Question (2 of 3: Extreme Values)
  89. 89 Harder SHM Question (1 of 5: Interpreting the question)
  90. 90 Harder SHM Question (2 of 5: Setting up the equations)
  91. 91 Harder SHM Question (3 of 5: Determining specific times)
  92. 92 Simple Harmonic Motion Question (3 of 3: Other Characteristics)
  93. 93 Harder SHM Question (4 of 5: Examining the geometry of movement)
  94. 94 Harder SHM Question (5 of 5: Determining specific speed)
  95. 95 Alternate Forms for Simple Harmonic Motion (Example 1 of 2)
  96. 96 Alternate Forms for Simple Harmonic Motion (Example 2 of 2)
  97. 97 Motion as Functions of Displacement (1 of 2: Why it matters)
  98. 98 Motion as Functions of Displacement (2 of 2: Example question)
  99. 99 Full Derivation of Acceleration = d(½v²)/dx
  100. 100 Using d(½v²)/dx without SHM (1 of 2: Understanding Velocity)
  101. 101 Using d(½v²)/dx without SHM (2 of 2: Reintroducing Time)
  102. 102 Using the d(½v²)/dx result (1 of 2: The vertical spring)
  103. 103 Using the d(½v²)/dx result (2 of 2: Rest Position & Max Speed)
  104. 104 Differential Equations for SHM (1 of 2: A curious pattern)
  105. 105 Differential Equations for SHM (2 of 2: Deriving v²=n²[a²-x²])
  106. 106 Projectile Motion (1 of 5: Defining Conditions for Projectile Motion and how time is built into it)
  107. 107 Projectile Motion (2 of 5: Outlining relationship between Initial v, x and y and projection angle)
  108. 108 Applications of Projectile Motion (1 of 4: Proving that two separate particles collide)
  109. 109 Projectile Motion (3 of 5: Defining the Acceleration, Velocity and Displacement Functions for x & y)
  110. 110 Projectile Motion (4 of 5: Finding max height using vertical velocity and displacement equations)
  111. 111 Projectile Motion (5 of 5: Finding Flight Time, Horizontal Range and Impact speed and angle)
  112. 112 Application of Projectile Motion (4 of 4: Proving that Path taken by projectile is a parabola)
  113. 113 Applications of Projectile Motion (2 of 4: Calculating V2, Collision Time & Place)
  114. 114 Applications of Projectile Motion (3 of 4: Finding the velocity the collision occurs at)
  115. 115 Harder Motion (2 of 2: Finding an expression for particle B to substitute time into to find x)
  116. 116 Harder Projectile Motion (1 of 5: Manipulating Trig Identities and finding time as a function of x)
  117. 117 Harder Projectile Motion (2 of 5: Substituting time expression to find velocity in terms of d)
  118. 118 Harder Projectile Motion (3 of 5: Finding what happens when theta approaches alpha and π/2)
  119. 119 Harder Projectile Motion (4 of 5: Finding a relationship between α & θ using Stationary Point)
  120. 120 Harder Projectile Motion (5 of 5: Using the second derivative to find the minimum value of θ)
  121. 121 Mechanics (1 of 7: Introduction to Forces and Newton's First Law and its relation to Mechanics)
  122. 122 Mechanics (2 of 7: Introduction to Newton's Second Law and Third Law and its relation to Mechanics)
  123. 123 Mechanics (3 of 7: Representing Physical Motion in mathematical terms)
  124. 124 Mechanics (4 of 7: Finding the angle subtended by the other line with the horizontal wall)
  125. 125 Mechanics (5 of 7: Resolving Forces to find the Horizontal forces acting on both strings)
  126. 126 Mechanics (6 of 7: Finding the Forces acting on the particle vertically)
  127. 127 Mechanics (7 of 7: Introductory Example to Mathematical Representation of Physical Motion)
  128. 128 Resisted Motion - Basic Example (1 of 2: Time as a function of Velocity)
  129. 129 Resisted Motion: Introductory Concepts
  130. 130 Resisted Motion - Basic Example (2 of 2: Further Manipulation & Conclusions)
  131. 131 Resisted Motion - Harder Example (1 of 2: Maximum Height)
  132. 132 Resisted Motion - Harder Example (2 of 2: End of the journey)
  133. 133 Intro to Straight Line Motion (1 of 3: Overview of language)
  134. 134 Intro to Straight Line Motion (2 of 3: Unpacking a basic question)
  135. 135 Intro to Straight Line Motion (3 of 3: Interpreting the equations)
  136. 136 Simple Harmonic Motion Example Question (1 of 3: Determining period of motion)
  137. 137 Simple Harmonic Motion Example Question (2 of 3: Solving for time)
  138. 138 Simple Harmonic Motion Example Question (3 of 3: Using graph symmetry)
  139. 139 SHM - Other Centres of Motion (1 of 2: Rearranging with trigonometric identities)
  140. 140 SHM - Other Centres of Motion (2 of 2: Determining attributes from the equation)
  141. 141 Functions of Displacement (1 of 3: Basic Simple Harmonic Motion)
  142. 142 Functions of Displacement (2 of 3: SHM with different centre)
  143. 143 Functions of Displacement (3 of 3: Straight line motion example)
  144. 144 Equation of Path (1 of 4: Establishing the horizontal equations)
  145. 145 Equation of Path (2 of 4: Deriving the Cartesian equation)
  146. 146 Equation of Path (3 of 4: Finding horizontal range)
  147. 147 Equation of Path (4 of 4: Example question)
  148. 148 Simple Harmonic Motion v² Equation (1 of 2: Deriving the result)
  149. 149 Simple Harmonic Motion v² Equation (2 of 2: Example question)
  150. 150 HSC Tide Question (1 of 3: Proving the time equation)
  151. 151 HSC Tide Question (2 of 3: Solving for time)
  152. 152 HSC Tide Question (3 of 3: Leaving the harbour safely)
  153. 153 Intro to Mechanics (1 of 4: Mathematics & physics)
  154. 154 Intro to Mechanics (2 of 4: Equations & kinematics)
  155. 155 Intro to Mechanics (3 of 4: Simple harmonic motion - foundations)
  156. 156 Intro to Mechanics (4 of 4: Basic SHM example)
  157. 157 Simple Harmonic Motion example (1 of 3: Interpreting given data)
  158. 158 Simple Harmonic Motion example (2 of 3: Forming an equation)
  159. 159 Simple Harmonic Motion example (3 of 3: Identifying the time of a given displacement)
  160. 160 Acceleration in terms of displacement (1 of 2: Explanation)
  161. 161 Acceleration in terms of displacement (2 of 2: Worked example)
  162. 162 Simple Harmonic Velocity via Displacement (1 of 2: Equating forms of acceleration)
  163. 163 Simple Harmonic Velocity via Displacement (2 of 2: Worked example)
  164. 164 Objects in Equilibrium (1 of 4: Comparing forces with displacement)
  165. 165 Objects in Equilibrium (3 of 4: Balancing vertical forces)
  166. 166 Objects in Equilibrium (2 of 4: Using trigonometric relationships)
  167. 167 Objects in Equilibrium (4 of 4: Worked exam question)
  168. 168 Concurrent Forces - Non-Equilibrium (2 of 3: Worked example)
  169. 169 Concurrent Forces - Non-Equilibrium (1 of 3: Introduction)
  170. 170 Concurrent Forces - Non-Equilibrium (3 of 3: Finding magnitude & direction)
  171. 171 Horizontal Resisted Motion (1 of 3: Introduction)
  172. 172 Horizontal Resisted Motion (2 of 3: Velocity in terms of displacement)
  173. 173 Horizontal Resisted Motion (3 of 3: Locating eventual resting place)
  174. 174 Plane Braking Model (3 of 3: Resetting the time variable)
  175. 175 Plane Braking Model (2 of 3: Considering reverse thrust)
  176. 176 Plane Braking Model (1 of 3: Constant frictional force)
  177. 177 Vertical Resisted Motion (5 of 5: How long till it returns to the ground?)
  178. 178 Vertical Resisted Motion (4 of 5: Finding v = f(t) by integration)
  179. 179 Vertical Resisted Motion (3 of 5: Determining the maximum height)
  180. 180 Vertical Resisted Motion (2 of 5: Finding y = f(v) by integration)
  181. 181 Vertical Resisted Motion (1 of 5: Introduction)
  182. 182 Terminal Velocity (1 of 2: Balancing forces)
  183. 183 Terminal Velocity (2 of 2: Determining drop height)
  184. 184 Resisted Projectile Motion (1 of 4: Understanding horizontal motion)
  185. 185 Resisted Projectile Motion (2 of 4: Understanding vertical motion)
  186. 186 Resisted Projectile Motion (3 of 4: Finding cartesian equation)
  187. 187 Resisted Projectile Motion (4 of 4: Determining equations from first principles)
  188. 188 Quadratic Drag (1 of 3: Evaluating the drag coefficient)
  189. 189 Quadratic Drag (2 of 3: Investigating horizontal motion)
  190. 190 Quadratic Drag (3 of 3: Determining the angle of projection)
  191. 191 Proving simple harmonic motion (Exam Question 1 of 10)
  192. 192 Finding maximum speed of SHM (Exam Question 2 of 10)
  193. 193 Forces on a hanging object (Exam Question 5 of 10)
  194. 194 Mechanics of a falling object (Exam Question 10 of 10)

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