Calculus in Mechanics

Example 1

Example 1 Video

Solving Differential Equations

Example 2

Example 2 Video

A note on integration

Acceleration and Velocity

Proof 3

Proof 3 Video

Example 4

Example 4 Video

Example 5

Example 5 Video

Example 6

Example 6 Video

Exercise 6.1

Exercise 6.1 Solutions

Further Motion in a Straight Line

Unit of Force

Newton's Laws

Example 1

Example 1 Video

Example 2

Example 2 Video

Gravity

Example 3

Example 3 Video

Exercise 6.2

Exercise 6.2 Solutions

Understanding Simple Harmonic Motion

Terminology and Definitions

Equations of Motion

Proof 1

Proof 1 Video

The Purpose of n and alpha in the Equation of Motion

Example 2

Example 2 Video

Example 3

Example 3 Video

Example 4

Example 4 Video

Example 5

Example 5 Video

Graphs of SHM

Example 6

Example 6 Video

Example 7

Example 7 Video

Exercise 6.3

Exercise 6.3 Solutions

Alternative Equations of Motion

Example 1

Example 1 Video

Velocity as a Function of Displacement

Proof 2

Proof 2 Video

Example 3

Example 3 Video

Example 4

Example 4 Video

Example 5

Example 5 Video

Exercise 6.4

Exercise 6.4 Solutions

Horizontal Resisted Motion

Resistance and how it is Modelled

Example 1

Example 1 Video

Explaining Example 1

Example 2

Example 2 Video

Explaining Example 2

Example 3

Example 3 Video

Explaining Example 3

Exercise 6.5

Exercise 6.5 Solutions

Vertical Resisted Motion

Constant Gravitational Acceleration

Terminal Velocity

Understanding Terminal Velocity

Example 1

Example 1 Video

Explaining Example 1

Example 2

Example 2 Video

Exercise 6.6

Exercise 6.6 Solutions

Cartesian Equations in Extension 1

Example 1

Example 1 Video

Cartesian Equations in Extension 2

Proof 2

Proof 2 Video

Example 3

Example 3 Video

Example 4

Example 4 Video

Example 5

Example 5 Video

Exercise 6.7

Exercise 6.7 Solutions

Particles that Rise then Fall

Example 1

Example 1 Video

Resisted Motion at an Angle to the Horizontal

Example 2

Example 2 Video

Splitting Air Resistance into Components

Quadratic Drag

Vertical and Horizontal Acceleration

Example 3

Example 3 Video

A Note on Example 3

Exercise 6.8

Exercise 6.8 Solutions