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Question Number 11998 by ajfour last updated on 09/Apr/17

Commented by ajfour last updated on 09/Apr/17

$W h a t d i s t a n c e d o e s p o i n t P$ $t r a v e l a s t h e c e n t r e m o v e s$ $f o r w a r d b y 2 π R . T h e d i s c$ $r o l l s w i t b o u t s l i p p i n g .$
Commented by mrW1 last updated on 10/Apr/17

$l e n g t h o f t r o c h o i d (r ⩽ R)$ $L = \int_{0}^{2 π} \sqrt{R^{2} + r^{2} - 2 R r \cos θ} d θ$
Commented by ajfour last updated on 10/Apr/17

$t h a n k s, t h i s i s t r u e b u t c o u p l e$ $o f m o n t h s b a c k y o u e x p l a i n e d$ $s o l u t i o n t o t h i s i n t e g r a l a s w e l l .$ $t h a t d i n t s e e m t o m a t c h w i t h$ $t h e c a s e r = R e v e n; f o r w h i c h$ $t h e a n s w e r i s L = 8 R . K i n d l y$ $s o l v e t h i s i n t e g r a l t o o . .$
Commented by mrW1 last updated on 10/Apr/17

$F o r r \neq R t h e i n t e g r a l i s n o t e a s y .$ $I n W o l f r a m y o u c a n r e a d m o r e d e t a i l s .$
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