Central Forces Notes Section 7

• Review of polar coordinates and how to graph an equation in polar coordinates
• Students are given the following diagram and asked to write down the position vector in polar coordinates on their small white boards
• Students are sometimes confused about the ellipse drawn on the board. They often think it is a 3D perspective drawing of a circle rather than an ellipse drawn in the plane of the board. It is important to clarify this.
• Some useful questions to get the students thinking about the differences between $\Vec {r}$, $\hat {r}$ and $\hat {\phi}$ are:
  1. Where is the tail of the position vector $\Vec {r}$ anchored?
  2. What about $\hat {r}$ and $\hat {\phi}$?

• It is often helpful to students if we emphasize that $\Vec {r}$ always points from the origin, but that $\hat {r}$ and $\hat {\phi}$ have their tails at the tip of the position vector $\Vec {r}$.