Rolling Billiards Ball: Applying friction (Computer simulation)

In summary: Your Name]In summary, Richard is working on a Billiards simulation and has encountered issues with the rotational and translational motion of the ball not matching up. He has researched and found helpful resources, but is struggling with correctly calculating the frictional forces involved. He has noticed an error in the article he referenced and suggests using the perpendicular distance instead of the radius to calculate the torque due to friction. He also mentions the importance of considering the angle of the surface and the coefficient of friction when calculating the frictional force, as well as the moment of inertia of the ball. Richard is seeking advice and assistance in troubleshooting his code and solving the issue.
  • #1
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Greetings to all

I apologise if this has already come up before, I found many related topics on these forums but nothing dealing with my specific problem (providing it is due to a physics error and not a programming one).

I'm currently in the midst of programming the physics part of a Billiards simulation. I've found this link http://archive.ncsa.uiuc.edu/Classes/MATH198/townsend/math.html to be quite helpful, but I've run into problems with basic ball movement.

I can determine when the ball begins rolling naturally and adjust the friction coefficients accordingly, but from what I've read the velocity of the point on the ball in contact with the table is zero when rolling naturally(which makes sense). So, instead of using the perimeter velocity at the point of contact to determine the frictional force direction (normalise + invert), I just use the individual linear and angular velocity vectors in order to calculate the corresponding frictional force and torque. I do this by taking the velocity at the point of contact ( angular or linear ), normalising and inverting it, and then scaling it by the ball's mass, gravitational acceleration and rolling friction (0.01), in the case of angular velocity I then calculate the corresponding torque.

My problem is that when I test my code, the rotational and translational motion don't match up, the rotation diminishes faster than the translational movement (so that the ball appears to slide just before stopping). I'm at a loss as to why this would be the case so I'm guessing I'm not correctly calculating the frictional forces. To reiterate I use the methods outlined in the article I pasted (there appears to be an error in article for calculating the torque due to friction, the radius(value, not the vector) shouldn't be used to calculate the force, I think)

Thanks in advance for all and any help,
Richard.
 
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  • #2


Hello Richard,

Thank you for posting your question on our forum. It sounds like you have already done some research and have a good understanding of the principles involved in simulating billiards. However, it seems like you may be encountering some issues with your calculations.

Firstly, I would like to mention that it is always a good idea to double check your calculations and equations when encountering unexpected results. In this case, I would suggest going through your code and equations step by step to see if you can identify any potential errors. It may also be helpful to compare your code with other sources or seek advice from other programmers or physicists.

Secondly, I would like to address the issue you mentioned with the torque calculation in the article you referenced. I agree with your observation that the radius should not be used to calculate the force. Instead, you should use the perpendicular distance from the point of contact to the center of mass.

Additionally, when calculating the frictional force, make sure you take into account the angle of the surface and the coefficient of friction. The angle of the surface will affect the magnitude of the frictional force, while the coefficient of friction will determine the direction of the force.

It is also important to consider the moment of inertia of the ball when calculating the torque due to friction. This will affect the rotational motion of the ball.

I hope these suggestions help you in troubleshooting your code and solving your problem. If you have any further questions, please don't hesitate to ask. Good luck with your simulation!
 
  • #3


Hello Richard,

Thank you for sharing your experience and question with us. I am always interested in discussing and solving problems related to physics and simulations.

From what you have described, it seems like you have a good understanding of the basics of friction and its effects on rolling billiard balls. However, I believe the issue you are facing may be due to a programming error rather than a physics one.

I would suggest checking your code and calculations again to make sure they are accurate. You may also want to consider seeking help from a physics or programming expert who can review your code and provide further insight.

Additionally, you may want to try running your simulation with different values for the friction coefficient to see if that affects the rotation and translational motion of the ball. This can help you narrow down the potential source of the error.

Overall, I encourage you to keep exploring and experimenting with your simulation to find the root cause of the issue. I am confident that with determination and a thorough understanding of physics principles, you will be able to solve this problem and create a successful rolling billiards simulation.

Best of luck to you in your scientific endeavors.
 

1. How does friction affect the motion of a rolling billiards ball?

Friction is a force that opposes motion, so it affects the motion of a rolling billiards ball by slowing it down. As the ball moves, it experiences friction from the surface it is rolling on, which causes it to lose energy and eventually come to a stop.

2. How does the surface affect the amount of friction on a rolling billiards ball?

The surface that the ball is rolling on can greatly affect the amount of friction it experiences. Rough surfaces, such as a carpet, will cause more friction and slow the ball down faster, while smoother surfaces, like a polished wood floor, will have less friction and allow the ball to roll for a longer distance.

3. Can friction be used to control the direction of a rolling billiards ball?

Yes, friction can be used to control the direction of a rolling billiards ball. By applying a force in a specific direction, such as hitting the ball with a cue stick, the friction between the ball and the surface can cause it to change direction.

4. How does the mass of a rolling billiards ball affect the amount of friction it experiences?

The mass of a rolling billiards ball does not directly affect the amount of friction it experiences. However, a heavier ball will have more inertia and require more force to start rolling, which can affect the amount of friction it experiences over time.

5. How can a computer simulation be used to study the effects of friction on a rolling billiards ball?

A computer simulation can be used to study the effects of friction on a rolling billiards ball by creating a virtual environment where different variables, such as surface type and force applied, can be controlled and tested. This allows for a more controlled and repeatable experiment compared to real-life scenarios.

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