Rigid Body Dynamics: balls colliding

[AndersLau]

Homework Statement

I want to analyse two colliding balls, rolling flat on a billiard table.
I have recorded two collisions from above the table. A 1D collision and a 2D collision.
In both collisions only 1 of the balls are rolling before the collision.

Known is:
mass of the balls: m₁=207g, m₂=203g
their radius: r=3cm
friction between table and balls: F₁=0.47N, F₂=0.46N
The velocity of the balls right before and after the collision.
I'm supposed to be using some physics on rigid body dynamics. From the video you can see, that even though the collision is in 1D, the rolling ball keeps rolling after it has hit the other. My 1 question is, does the rolling ball transfer all of its translational energy, and keeps all the rotational itself? Or how does it work?

In which other ways could i analyze these situations?

Thank you.

 

[PeterO]

Homework Statement

I want to analyse two colliding balls, rolling flat on a billiard table.
I have recorded two collisions from above the table. A 1D collision and a 2D collision.
In both collisions only 1 of the balls are rolling before the collision.

Known is:
mass of the balls: m₁=207g, m₂=203g
their radius: r=3cm
friction between table and balls: F₁=0.47N, F₂=0.46N
The velocity of the balls right before and after the collision.



I'm supposed to be using some physics on rigid body dynamics. From the video you can see, that even though the collision is in 1D, the rolling ball keeps rolling after it has hit the other. My 1 question is, does the rolling ball transfer all of its translational energy, and keeps all the rotational itself? Or how does it work?

In which other ways could i analyze these situations?

Thank you.

In a normal billiards game the cue ball certainly retains its rotational momentum after collision. In that way the [very] skillful player is able to cause the cue ball to move to just about any position they wish, after striking the other ball.

Even less skilled amateurs can use back spin, top spin and side spin to make the cue ball jag off in a desired direction - including coming back towards the player.
Indeed it takes a fair amount of skill to ensure the cue ball has no spin at all when it strikes the target ball.

 

[AndersLau]

okay, thank you.
Do you have any relevant calculations in mind? I find it a little tough.

 

[PeterO]

okay, thank you.
Do you have any relevant calculations in mind? I find it a little tough.

Not really - though conservation of momentum says that without a head on collision, the cue ball can't stop completely.

 

[asteriatic]

I would like to provide some insights on the topic of rigid body dynamics and the specific scenario of balls colliding on a billiard table.

Firstly, it is important to understand that rigid body dynamics deals with the motion and interactions of objects that maintain their shape and size. In this case, the balls can be considered as rigid bodies since they maintain their shape and size during the collision.

Now, let's address the question about the transfer of energy during the collision. In a perfectly elastic collision, the total kinetic energy of the system (both balls) is conserved. However, in a real-world scenario, there will always be some energy lost due to factors such as friction, deformation of the balls, and air resistance. This means that the total kinetic energy after the collision will be slightly less than the total kinetic energy before the collision.

In terms of the transfer of energy between translational and rotational motion, it depends on the specific conditions of the collision. If the collision is perfectly elastic and the balls have the same mass and radius, then the rolling ball will transfer all of its translational energy to the other ball and keep all of its rotational energy. However, if there is any imbalance in mass or radius, then there will be some transfer of both translational and rotational energy between the balls.

To analyze this situation, you can use the principles of conservation of momentum and conservation of energy to calculate the velocities of the balls before and after the collision. You can also consider the effects of friction and the rotational inertia of the balls in your analysis.

Other ways to analyze this scenario could include using computer simulations or conducting experiments with different conditions (e.g. different masses or radii of the balls) to observe the effects on the collision. Overall, there are various approaches that can be used to analyze rigid body dynamics and collisions, and the most appropriate method will depend on the specific goals and limitations of the study.