# Velocity in plane polar coordinates

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

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

Thanks

## Answers and Replies

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##.

Thanks!