# Deceleration over a distance

1. Jun 6, 2005

### PhilippeIngels

I have a roulette wheel and a ball spinning in opposite directions

First I need to know how to calculate the deceleration of the wheel if I want it to stop over a distance of 370 degrees. I have d, Vi, and Vf=0. I have this formula which seems to work but does not look right:

this.wheelDeceleration = (this.wheelInitSpeed/this.wheelStopDistance)*2;

Then I need to know how to calculate the ball's deceleration so its final velocity will be 0.2 when it reaches to winning slot. I know the distance to the winning slot, I know the velocity of the ball and the velocity of the wheel. I also know the wheel's constant deceleration (a).

The trick is the fact that the wheel is also decelerating and that's where I'm stuck.

Thanks

Philippe
__________________

2. Jun 6, 2005

### gerben

This should be:
this.wheelDeceleration = (this.wheelInitSpeed*this.wheelInitSpeed)/(2*this.wheelStopDistance);
or
this.wheelAcceleration = -(this.wheelInitSpeed*this.wheelInitSpeed)/(2*this.wheelStopDistance);

$$a_{wheel} = \frac{-v_{wheel}^2}{2d_{wheel}}$$

I assume that you calculate the motion of the ball relative to the wheel.
In that case the acceleration of the ball would be:

$$a_{ball} = \frac{0.04-v_{ball}^2}{2d_{ball}}$$

You can combine the acceleration of the ball with the acceleration of the wheel in case you want to know the acceleration of the ball relative to the table. Because the ball moves in opposite direction than the wheel the acceleration of the ball relative to the table would be:

$$a_{ball}-a_{wheel}$$

3. Jun 7, 2005

### PhilippeIngels

Thanks

Thank you very much for your help. I really appreciate it.

4. Apr 20, 2008

### fabiolone

Hello, i'm an italian newbie and i'm sorry for my bad english.
first of all I don't understand what is d, Vi and Vf
I suppose d is the distance (what distance?), Vi is the instant velocity and Vf is the final velocity.

I would like to know:

1) in what measure units are expressed these values?
2) what is the meaning of "wheel stop distance"?

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I am trying to study the roulette physical and i have other questions to place.
I know this data:
1. the time that employs the ball to complete first round (this is T1) expressed in milliseconds
2. the time that employs the ball to complete second round (this is T2) expressed in milliseconds
3. the time that employs the ball to complete last round (this is Tf) expressed in milliseconds
4. the time that employs the rotor of the wheel to complete a round (this is Tr) expressed in milliseconds
I would like to know:
1. the ball's deceleration (dB)
2. the rotor's deceleration (dR)
3. the part of the rotor that finds when the ball completes the last round (Tf)

This could be an example:

T1 = 800 ms/round
T2 = 890 ms/round
Tf = 2160 ms/round
Tr = 6142 ms/round