Solving the Physics Problem: Modeling a Spinning Ball Dropped on Floor

[NotMrX]

Hello

Does anyone know how to model a ball (sphere) with mass spinning with an initial angular velocity that gets dropped on the floor with a coefficient of friction? And find the final angular velocity?

I tried solving the problem but somehow I got a singularity.

The idea I used was the work from friction equals the change in the kinetic energy (rotational and translational) but even after I reworked I got a singularity so i must be doing something wrong.

Thanks for your help.

 

[berkeman]

Do you mean like a spinning billiard ball or a spinning rubber ball? How much does the ball deform on impact? It seems that for a rubber ball, some energy will get converted to head from the deformation and rebound. Even the billiard ball example will deform slightly during the bounce.

 

[J Hann]

There 3 ways to solve problem: straightforward application of Newton's laws, conservation of energy, and conservation of momentum. Conservation of momentum is by far the easiest. The angular momentum of the ball when it is released equals the angular momentum when the ball starts to roll (linear momentum + rotational momentum). You can check your result using the general solution:

Omega final = Omega initial / (I + mr^2 / I)

Example: Spinning hoop - Omega final = Omega initial / 2