[Oblarg]

Originally Posted by James Kuszmaul

I'm not entirely sure what you mean by trying "to calculate from the forces themselves" (I only mentioned a force at all so that I could create the equivalency; there may be some convenient equation that already takes that into account). My issues resulted from a couple of silly mental errors in typing out the solution (I shouldn't solve equations in text editors).

I was trying to get at that if you place your origin on the floor, you can notice that the friction force is pointing towards the origin and thus angular momentum is conserved; you need not not consider any forces in any capacity past that, only the initial and final velocities.

Originally Posted by seg9585

Assuming a solid sphere, I get a final velocity v2 = 5/7*v1

Using conservation of momentum:

m*v1*R = I*omega
omega = v2/R (ball rolling v2 = r*omega)

I = I_sphere + I_point mass = 2/5*m*R^2 + m*R^2 = 7/5*m*R^2 (parallel axis theorem)

m*v1*R = 7/5*m*R^2 * v2/R
m, R both cancel

v1 = 7/5*v2 --> v2 = 5/7*v1

This is correct.