Question Number 2158 by Yozzis last updated on 05/Nov/15
$${Find}\:{the}\:{ratio},\:{over}\:{one}\:{revolution},\:{of}\:{the}\:{distance}\:{moved}\:{by} \\ $$$${a}\:{wheel}\:{rolling}\:{on}\:{a}\:{flat}\:{surface}\:{to}\:{the}\:{distance}\:{traced}\:{out}\:{by} \\ $$$${a}\:{point}\:{on}\:{its}\:{circumference}.\: \\ $$
Commented by ssahoo last updated on 06/Nov/15
$$\mathrm{Wheel}\:\mathrm{distance}=\mathrm{2}\pi{r} \\ $$$$\mathrm{point}\:\mathrm{on}\:\mathrm{perimeter}\:\mathrm{will}\:\mathrm{be}\:\mathrm{arc}\:\mathrm{length}\:\mathrm{of}\:\mathrm{cycloid} \\ $$$${x}={r}\left({t}−\mathrm{cos}\:{t}\right) \\ $$$${y}={r}\left(\mathrm{1}−\mathrm{sin}\:{t}\right) \\ $$$${t}\:\mathrm{from}\:\mathrm{0}\:\mathrm{to}\:\mathrm{2}\pi \\ $$$$\mathrm{Arc}\:\mathrm{length}:\:\mathrm{8}{r} \\ $$
Commented by Yozzis last updated on 06/Nov/15
$${Thanks} \\ $$