Day 53 in MAT229

Uniform Circular Motion is best understood using the concepts of vector geometry.
So are many other concepts from physics, where quantities have a direction and a "strength" -- a rocket in flight, for example. It is moving in a certain direction, and it has a speed, whose value can be represented by the length of a vector.
- vector: a quantity with length and direction:
- In uniform circular motion, we could represent the position of the bob by parametric equations ${x(t)=R\cos({t})}$ and ${y(t)=R\sin({t})}$
  We then combine these into one quantity, the vector ${{\langle}x({t}),y({t}){\rangle}}$ .
- The three vectors that are (most) important in the physics of circular motion are the vectors of
  - position ${{\langle}x({t}),y({t}){\rangle}}$
  - velocity ${{\langle}x'({t}),y'({t}){\rangle}}$
  - acceleration ${{\langle}x''({t}),y''({t}){\rangle}}$
  each of which is a function of time.
- Animations, demonstrations:
  - Uniform Circular Motion
    For all of the gory details, a nice layout of all the physics, and a cool (but scary) example -- the Australian dialect makes it more fun, too!