ENSC2004 - Lecture 1

Part 1 - Slides
Part 2 - Slides

Mechanics is the area of physics concerned with the relationships between force, matter and motion among physical objects
- The sub-area that focuses on motion is known as kinematics

Particle
We may treat a body as a point mass when its dimensions are irrelevant to the description of its position, and actions of the forces applied to it.
It does not necessarily mean we are dealing with a tiny object.
Rigid Body
We refer to an object as a rigid body when its dimension are important and where the deformation of the object is likely to be negligible for the purposes of the analysis.
Concentrated Forces
All forces act over some finite area (or volume e.g. gravity).
A concentrated force is a convenient way to idealise a force where the area over which the load is applied is small relative to the overall size of the body

Objectives:
1. Resolve a 2D vector into components
2. Add two or more concurrent vectors together using scalar or cartesian notation

To split a vector into components, form a right angled triangle
- Components need to be at right angles to each other
  - i.e. components are always perpendicular
- Simple trig can be used to solve magnitude in $x$ and $y$ direction
- This can also be applied to finding components in non $x / y$ directions, however, the vector will represent a side of the triangle instead of the diagonal
Breaking vectors into components make them easy to add together
- Sum $i$ and $j$ components
- Then calculate: $i^{2} + j^{2}$ where $i$ and $j$ are the total magnitude in the $x$ and $y$ direction respectively
- This can be done for any number of vectors
2a: $θ = tan^{- 1} (\frac{j}{i})$ gives the angle between the vector and the $x$ -axis
- You may also see this: $θ = Atan 2 (j, i)$ which means the same thing
  - The two is needed to account for the quadrant of the vector

ENSC2004 - Lecture 2

Quartz 5