Module 1 : A Crash Course in Vectors
Lecture 2 : Coordinate Systems
  In the figure, the positions of a particle are shown at time $t$ and $t+ dt$. The unit vectors $\hat\rho$ is shown in red while the unit vector $\hat\theta$ is shown in blue. It can be easily seen by triangle law of addition of vectors that the magnitude of $\Delta\hat\rho $ and $\Delta\hat\theta$ is . However, as the limit $dt\rightarrow 0$, the direction of $\Delta\hat\rho $ is in the direction of $\hat\theta$ while that of $\Delta\hat\theta$ is in the direction of $-\hat \rho$. Thus
 
  Now, $d\theta/dt$ is the angular velocity of the point, which is usually denoted by $\omega$, Thus we have,
 
\begin{eqnarray*} \frac{d\hat\rho}{dt} &=& \omega\hat\theta\\ \frac{d\hat\theta}{dt}&=& -\omega\hat\rho \end{eqnarray*}
   
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