Colliding, spinning particles: Can it be solved?

[raisin_raisin]

Hi, I am trying to work out the result of a collision between two rotating particles if you knew all initial speeds, initial rotation speeds, masses etc. There is no friction or anything complicating.

COM: m₁v_1initial + m₂v_2initial = m₁v_1final + m₂v_2final.

COAM: I₁w_1initial + I₂w_2initial = I₁w_1final + I₂w_2finall.

COE: m₁v²_1initial + m₂v²_2initial + I₁w²_1initial + I₂w²_2initial = I₁w²_1final + I₂w_2finall + m₁v²_1final + m₂v²_2finall.

So 3 equations for 4 unknowns . Am I missing anything obvious? Is there another equation I could use was thinking trying to use L= r x mv ? Is there any assumptions I could make to simplify things?

Thanks for any help.

 

[jbsteele]

The equations you have given are sufficient to solve the problem. However, if you want to simplify it further, you could make assumptions such as the particles remaining in contact during the collision, or that the particles have equal mass and/or equal moment of inertia. This would reduce the number of unknowns and allow you to solve for the final velocities and angular velocities more easily. Additionally, you can use the conservation of energy and momentum to further simplify the problem.

 

[thomate1]

I would say that yes, it is possible to solve for the result of a collision between two rotating particles if you have all the initial information and there are no complicating factors such as friction. The equations you have listed are correct and can be used to solve for the final velocities and angular velocities of the particles after the collision.

However, it is important to note that these equations assume certain things, such as the particles being rigid bodies and the collision being perfectly elastic. In reality, there may be other factors at play that could affect the outcome of the collision. Additionally, it may be difficult to obtain all of the necessary initial information in a real-world scenario.

In terms of simplifying the equations, you could make certain assumptions, such as the particles having equal masses or equal initial angular velocities, which would reduce the number of unknowns and make the problem easier to solve.

Another approach could be to use conservation of momentum and conservation of energy in the center of mass frame, which would involve only two equations and may be easier to solve. Additionally, using the equation L = r x mv, as you suggested, could also be helpful in solving for the final angular velocities.

In conclusion, while it is possible to solve for the result of a collision between two rotating particles, it may require making certain assumptions and simplifications in order to obtain a solution.