Question: The involute of a circle (Figure 8), traced by a point at the end of a thread unwinding from a circular spool of radius R,

The involute of a circle (Figure 8), traced by a point at the end of a thread unwinding from a circular spool of radius R, has parametrization (see Exercise 29 in Section 11.2)

Find an arc length parametrization of the involute. String (length Ro) (R cos 0, R sin 0), R 0 P

r(0) = (R(cos0+ 0 sin), R(sin 0 - 0 cos 0))

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