2D Collisions with Friction and Rotation (identical cylindrical objects)

[RedHammer]

Hi,

I've been searching the internet for useful information regarding this but I cannot find anything that helps me completely. I am working on a project on my own where I have identical cylindrical objects (standing up on their flat sides like hockey pucks on ice - so from a 2D "overhead" perspective, they'd look like circles) and I need to determine all of the resultant components of a collision between two of them. Friction is critical (between an object and the ground, and between two objects) as well as the effect of the rotations of each object. The collisions are not quite perfectly elastic and can be from any angle (head-on or more to one side).

I need to find out what the equations are for the resulting velocities, angular velocities and movement angles after the collision, given that I know the initial velocities, angular velocities and the offset between their centers of mass when they collide. The objects are uniform throughout so their center of mass is in the very center.

I'm not a physics buff (obviously) but I need to determine the calculations for this project and I am really struggling to find the information I need. It's hard to find something with all of the realistic specifics that I require. Would anyone be able to help me?

Thank you very much.

 

[eljose79]

Hi there,

I can definitely help you with your project. The equations you are looking for are known as the conservation of momentum and conservation of angular momentum equations. These equations state that the total momentum and angular momentum of a system (in this case, the two cylindrical objects) before and after a collision must be equal.

In order to use these equations, you will need to know the initial velocities and angular velocities of the objects, as well as the mass and moment of inertia (a measure of an object's resistance to rotation) of each object. The offset between their centers of mass will also play a role in the calculations.

Additionally, you will need to consider the coefficient of friction between the objects and the ground, as well as between the two objects. This will affect the amount of energy lost during the collision and the resulting velocities and angular velocities.

I recommend looking into textbooks or online resources on the topic of collisions and conservation laws for more detailed explanations and examples. You may also want to consider using a physics simulation software to help you visualize and calculate the results of your collisions.

I hope this helps! Let me know if you have any further questions. Good luck with your project!

 

[astrokreng]

Hello,

I can understand your struggle to find the information you need for your project. The topic of collisions with friction and rotation can be quite complex and it is important to have a strong understanding of physics principles to accurately calculate the resultant components of such collisions.

To start, I would recommend looking into the principles of conservation of momentum and conservation of energy. These principles are crucial in understanding the behavior of objects during collisions. In your case, you will need to consider both translational and rotational motion of the objects involved in the collision.

Furthermore, it is important to take into account the coefficient of friction between the objects and the ground, as well as between the two objects. This will affect the amount of energy lost during the collision and ultimately impact the resulting velocities and angular velocities.

I suggest breaking down the problem into smaller, more manageable parts. For example, you can first calculate the linear momentum of the objects before and after the collision, then move on to calculating the angular momentum and rotational motion. You can also consider using vector diagrams to visualize the forces and velocities involved in the collision.

In terms of equations, there are several that can help you calculate the resultant velocities and angular velocities after the collision. Some of these include the conservation of momentum equation (m1v1 + m2v2 = m1v1' + m2v2'), the conservation of energy equation (1/2m1v1^2 + 1/2m2v2^2 = 1/2m1v1'^2 + 1/2m2v2'^2), and the equations for rotational motion (angular momentum = moment of inertia x angular velocity). You can also consider using the coefficient of friction in your calculations, such as in the equation for kinetic friction force (Ff = μN).

I hope this helps guide you in the right direction. It may also be helpful to consult with a physics teacher or tutor for further guidance and clarification. Good luck with your project!