Use the transformations relating polar and Cartesian coordinates to prove that [frac{d theta}{d t}=frac{1}{r^{2}}left[x frac{d y}{d t}-y

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Use the transformations relating polar and Cartesian coordinates to prove that

\[\frac{d \theta}{d t}=\frac{1}{r^{2}}\left[x \frac{d y}{d t}-y \frac{d x}{d t}\right]\]

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