Velocity in plane polar coordinates

[marcom]

Hi,
I have a problem with the following explanation of velocity in plane polar coordinates.

I don't understand why the magnitude of Δe_r is approximately equal to Δθ.

Thanks

 

[Einj]

You know from basic geometry that the arc of circumference spanned by $\Delta \theta$ is going to be $\delta=|\hat{e}_r|\Delta\theta$. However, even if $\Delta e_r$ is actually straight, it is very very small and so it will be close in magnitude to the arc of length. Also since $\hat{e}_r$ has unit magnitude, you find $\Delta e_r\simeq\delta=\Delta\theta$.

 

[marcom]

Thanks!