Circular Motion Centripetal Acceleration Arc Length

One day a little kid is playing with a yo-yo and swinging it around in a circle for his own amusement.

Suddenly a crazed physicist walks up and decides to explain the physics of the circular motion.

First he asks the kid to spin the yo-yo around without any acceleration and the kids tries, but this turns out to be a trick question since there always is an acceleration towards the center (centripetal or center seeking force) because the velocity changes directions.

The physicist next shows how components can be used for measuring velocity vectors.

He then explains that describing certain aspects of circular motion with rectangular coordinates is pure silliness and that sometimes polar coordinates with an angle and a radius are much simpler.

He notes however that unlike in navigation, the angle is measured from the positive x-axis in physic.

Finally the physicist gives a nifty trick (s=rφ) for finding the arc length of pizza, or any circle, if one knows the radius and angle phi, but speaking of pizza he thinks about how good some would be and walks off.