Need Help Understanding Cycloid Rolling vs Slipping

[shoushou]

Hi everyone,
i have a problem concerning with the reason to why taking the cycloid to be parametrised by (sin(t)-t, cos(t)+1) causes it to roll, whereas taking (sin(t)-at, cos(t)+1) for a is not quals to 1, would cause it to slip.


can anybody explain to me or give me a hint, thanks a lot.

 

[tiny-tim]

Welcome to PF!

Hi everyone,
i have a problem concerning with the reason to why taking the cycloid to be parametrised by (sin(t)-t, cos(t)+1) causes it to roll, whereas taking (sin(t)-at, cos(t)+1) for a is not quals to 1, would cause it to slip.

Hi shoushou! Welcome to PF!

Hint:

i] from each of the equations, how far has the circle gone when it completes a 360º revolution?

ii] how far does it need to go to avoid slipping?

iii] then prove it for smaller angles.