Chapter 14, Problem 64RE

a.

To determine

To explain: The reason for the spiral $r=\frac{t\theta }{\left(2\pi \right)}$, where $0\le \theta \le 2\pi N$ has N loops, $R=Nt$ units is the radius of the entire spiral and to sketch the three loops of the spiral.

b.

To determine

To find: The length of the spiral $r=\frac{t\theta }{\left(2\pi \right)}$, where $0\le \theta \le 2\pi N$.

c.

To determine

To show: The length is $L\approx t\pi N^2=\frac{\pi R}{t}$ by simplifying the integral of the length obtained in part b.

d.

To determine

To find: The limits of the integration.