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# Kinematics in Polar Coordinates

## Prerequisites

- Students should have some familiarity with polar coordinates
- Students should be familiar with the product rule for differentiation

## In-class Content

- Spherical and Polar Coordinates Review
- Position Vectors in Polar Coordinates (Lecture/Discussion, 15 minutes)
- Velocity and Acceleration in Polar Coordinates (Small Group Activity, 20 minutes)
- Kepler's 2nd Law in Polar Coordinates (Lecture, 5 minutes)

## Homework for Polar Coordinates

- (LinePolar)
*Gain some experience with polar equations.*The general equation for a straight line in polar coordinates is given by: $$r(\phi)=\frac{r_0}{\cos(\phi-\delta)}$$ Find the polar equation for the following straight lines:

$y=3$

$x=3$

$y=-3x+2$

- (PolarSpherical)
*A short problem to check your geometric understanding of the relationship between spherical and polar coordinates.*Show that the plane polar coordinates we have chosen are equivalent to spherical coordinates if we make the choices:

- The direction of $z$ in spherical coordinates is the same as the direction of $\Vec L$.
- The $\theta$ of spherical coordinates is chosen to be $\pi/2$, so that the orbit is in the equatorial plane of spherical coordinates.