Chapter 6.3, Problem 12E

Interpretation Introduction

Interpretation:

To show that $\dot{\text{θ}}\text{ =}\frac{\left(\text{x}\dot{\text{y}}\text{ - y}\dot{\text{x}}\right)}{{\text{r}}^{\text{2}}}$ using the identity ${\text{θ = tan}}^{\text{-1}}\left(\frac{\text{y}}{\text{x}}\right)$.

Concept Introduction:

Polar coordinates in terms of Cartesian can be written as $\text{x = r cosθ}$ and $\text{y = r sinθ}$.

In Cartesian coordinates the polar coordinate r is given by $\text{r = }\sqrt{{\text{x}}^{\text{2}}{\text{+y}}^{\text{2}}}$.