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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.
