Module 1 : A Crash Course in Vectors
Lecture 2 : Coordinate Systems

Example 2 :

A vector $\vec A$has cartesian components $A_x$and $A_y$. Write the vector in terms of its radial and tangential components.

Solution :

Let us write

\begin{displaymath}\vec A = A_\rho\hat\rho + A_\theta \hat\theta\end{displaymath}

Since $\hat\rho$and $\hat\theta$are basis vectors $\hat\rho\cdot\hat\rho = \hat\theta\cdot\hat\theta =1$and $\hat\rho\cdot\hat\theta = 0$. Thus

\begin{displaymath}A_r = \vec A\cdot\hat\rho,\ \ \ A_\theta=\vec A\cdot\hat\theta\end{displaymath}

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