Applications of Calculus to Mechanics

Explore the applications of calculus in mechanics through this comprehensive 8-hour video series. Delve into topics such as circular motion, conical pendulums, banked tracks, and the physics of cycling. Learn to derive equations of path, understand angular and linear velocity, and analyze uniform and non-uniform circular motion. Master force equations, tension calculations, and problem-solving techniques for various mechanical systems. Investigate real-world scenarios like discus throws, weightlessness simulators, and optimum speeds on banked tracks. Develop a deep understanding of rotational dynamics, resolving forces, and the interplay between geometry and motion. Perfect for students and enthusiasts seeking to enhance their knowledge of applied calculus in mechanical systems.

Equation of Path: Derivation.
Equation of Path: Simple Example.
Introduction to Circular Motion: Angular & Linear Velocity.
Uniform Circular Motion - Direction of Acceleration (1 of 2: Adding Vectors Visually).
Uniform Circular Motion - Direction of Acceleration (2 of 2: Force Equations).
Uniform Circular Motion: Determining Tangent & Normal Forces.
Force Equations for Uniform & Non-Uniform Circular Motion.
Uniform Circular Motion: Basic Example Question.
Uniform Circular Motion: Tension & Tensile Strength.
The Conical Pendulum (1 of 2: Understanding the Forces).
General Purpose Algorithm for Mechanics Questions.
The Conical Pendulum (2 of 2: Determining Tension, Angle & Height).
Pendulum on Surface of Cone (1 of 2: Tension & Normal Force).
Pendulum on Surface of Cone (2 of 2: Determining Maximum Velocity).
Conical Pendulum Inside a Bowl (1 of 2: Setting up the question).
Conical Pendulum Inside a Bowl (2 of 2: An unexpected change in tension).
Introduction to Banked Tracks (1 of 2: What are they?).
Banked Tracks: Example Question.
Introduction to Banked Tracks (2 of 2: Optimum Speed & Height).
The Inclined Cyclist (1 of 2: Explanation & Question).
The Inclined Cyclist (2 of 2: Friction & Angle).
Interesting Circle Geometry / Motion Question (1 of 2: Internal Angular Velocities).
Interesting Circle Geometry / Motion Question (2 of 2: External Angular Velocity).
Circular Motion (1 of 6: Understanding Rotation).
Circular Motion (2 of 6: The Discus Throw).
Circular Motion (3 of 6: Basic Example Question).
Circular Motion (4 of 6: Resolving Forces).
Circular Motion (5 of 6: Force Along the Normal).
Circular Motion (6 of 6: Force Along the Tangent).
Uniform Circular Motion examples (1 of 2: Finding angular velocity & acceleration).
Uniform Circular Motion examples (2 of 2: On a flat surface).
Angular Velocity with Non-Circular Motion.
Intro to Conical Pendulum (1 of 2: Vertical & Horizontal Motion).
Understanding Weightlessness in a Simulator.
Intro to Conical Pendulum (2 of 2: Understanding Tension).
Walkthrough of Conical Pendulum Question (1 of 2: Working out the path).
Walkthrough of Conical Pendulum Question (2 of 2: Calculating Period & Tension).
Conical Pendulum Example (1 of 2: Finding radius of circular motion).
Conical Pendulum Example (2 of 2: Finding angular velocity & tension).
Banked Tracks (1 of 5: Why they're needed).
Banked Tracks (2 of 5: How they're useful).
Conical Pendulum on a Conical Surface (1 of 2: Initial Geometry).
Conical Pendulum on a Conical Surface (2 of 2: Resolving Forces).
Conical Pendulums on Various Surfaces.
Banked Tracks (3 of 5: Resolving forces).
Banked Tracks (4 of 5: Concrete example).
Banked Tracks (5 of 5: Understanding lateral force).
The Leaning Cyclist (1 of 4: Introduction).
The Leaning Cyclist (2 of 4: Simplified Model).
The Leaning Cyclist (3 of 4: Torque).
The Leaning Cyclist (4 of 4: A Better Model).