Roulette Problem: Answers for Ball Spin and Cone Relationship

  • Thread starter AdultJason
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In summary, the problem states that a roulette ball spins in a groove of a cone until the gravitational force pulling it down exceeds the force created by its spin. The ball's diameter is greater than the groove's thickness. The time the ball leaves the groove depends on its original angular velocity and the deceleration caused by the resistance between the ball and the groove. The wheel rotates in the opposite direction to the ball's revolution in roulette.
  • #1
AdultJason
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Hello,

Can you help by providing some answers to a Roulette problem I have.

The problem is that a roulette ball spins in the grove of a cone until the power pulling it down exceeds the force created by the push of the spin of the ball. Also, the diameter of the ball exceeds the thickness of the grove.

If the above is true, then does a relationship exist between where the ball leaves the grove, which is dependent on the force put into the spin as well as the starting point of the spin and a certain co-ordinate on the cone that the ball will cross as it rotates downwards?

Any help will be much appreciated.
 
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  • #2
The time when the ball leaves the groove would depend in its original angular velocity. To fall out of the groove, the gravitational force pulling the ball down or out of the groove, must exceed the centripetal force keeping the ball in place.

The ball travels in opposition to the spin of the cone, so the ball must be decelerating at some rate.


So, [itex]\omega (t) = \omega_o + \alpha * t[/itex], where

[itex]\omega[/itex] = angular velocity of ball
[itex]\omega_o[/itex] = initial angular velocity
[itex]\alpha[/itex] = angular acceleration, which is negative (-) for deceleration

This equation implies that angular acceleration is constant.

If not then the deceleration becomes

[itex] \int^t_{t_o}{\alpha(t)} dt[/itex], and to may = 0.

The deceleration would depend on the resistance between the ball and the groove, and the relative speed between the ball and the groove. In rouloutte the wheel rotates in the opposite direction to the revolution of the ball.
 
Last edited:
  • #3
Thank you.

Hello,

Thank you for reaching out with your Roulette problem. The relationship between the ball leaving the groove and a certain coordinate on the cone can be determined by the angle of the cone and the speed of the ball's spin.

The angle of the cone will determine the rate at which the ball rotates downwards, and the speed of the ball's spin will determine the force needed to pull it down. If the force of the spin is greater than the force pulling it down, the ball will continue to spin in the groove. However, if the force pulling it down exceeds the force of the spin, the ball will leave the groove and move towards the bottom of the cone.

To determine the exact relationship between the ball leaving the groove and a specific coordinate on the cone, you will need to take into account the diameter of the ball and the thickness of the groove. This will help determine the point at which the ball will leave the groove and the angle at which it will cross a certain coordinate on the cone.

I hope this helps answer your question. Best of luck with your Roulette problem!
 

1. What is the Roulette problem?

The Roulette problem is a mathematical problem that involves predicting the outcome of a series of Roulette spins. It is based on the concept of probability and involves analyzing patterns and trends in the outcomes of previous spins to make predictions for future spins.

2. How is the Roulette problem solved?

The Roulette problem can be solved by using different mathematical methods such as probability theory, statistical analysis, and mathematical modeling. These methods help in understanding the patterns and trends in the outcomes of Roulette spins, which can then be used to make predictions for future spins.

3. Can the Roulette problem be solved with 100% accuracy?

No, the Roulette problem cannot be solved with 100% accuracy. This is because there are many factors that can affect the outcome of a Roulette spin, such as the speed of the wheel, the force of the spin, and the position of the ball. These factors make it impossible to predict the outcome of a spin with complete accuracy.

4. Is there a guaranteed strategy to win at Roulette?

No, there is no guaranteed strategy to win at Roulette. The game is based on chance and there is no way to predict the outcome of a spin with complete accuracy. While some strategies may increase your chances of winning, there is no guarantee that you will win every time.

5. How can I improve my chances of winning at Roulette?

While there is no guaranteed way to win at Roulette, there are some tips that can help improve your chances of winning. These include setting a budget and sticking to it, choosing a betting strategy that works for you, and being aware of the odds of different bets. It is also important to remember that Roulette is a game of chance and to gamble responsibly.

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