This is a diagram from my text:
All of the labels make sense except the $r \Delta \theta$ label on the inner edge of the shaded cell. Why is that the length of that side of the bent rectangle?
2026-03-29 23:09:36.1774825776
Why is the length of the inner edge of a cell in polar coordinates equal to $r \Delta \theta$?
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thats Pretty much the definition of radians. The perimeter of a circle of radius $r$ is $2\pi r$ and the arc length of any piece of a circle is then $2\pi r$ times the percentage of the circle that the arc constitutes. In this case, that percentage is $\frac{\Delta\theta}{2\pi}$