Physical model of the roulette wheel

[yamata1]

TL;DR Summary

I would like an explanation of the physical model for a roulette wheel.

Hello,
I am having trouble understanding the two friction force terms from the ball rolling on page 4 of this physical model: http://www.dewtronics.com/tutorials/roulette/documents/Roulette_Physik.pdf
What is the reason for the $cos\theta$ term ?

I think the frame of reference is made up of the weight vector and the centrifugal force vector,but the tilt angle epsilon is shown page 15.

Thank you.

 

[willem2]

I am having trouble understanding the two friction force terms from the ball rolling on page 4 of this physical model: http://www.dewtronics.com/tutorials/roulette/documents/Roulette_Physik.pdf
What is the reason for the $cos\theta$ term ?

I think the frame of reference is made up of the weight vector and the centrifugal force vector,but the tilt angle epsilon is shown page 15.

How the steepness of the wheel is affected by the til depends on the position on the wheel.
At the highest point of the tilt, $cos\theta$ = 1 and the angle that the surface of the wheel makes is $\delta + \epsilon$ at the opposite point of the wheel this angle is $\delta - \epsilon$

 

[yamata1]

How the steepness of the wheel is affected by the til depends on the position on the wheel.
At the highest point of the tilt, $cos\theta$ = 1 and the angle that the surface of the wheel makes is $\delta + \epsilon$ at the opposite point of the wheel this angle is $\delta - \epsilon$

Thank you for this explanation,it's clear now.