General question about torque of sphere

[dannee]

Homework Statement

if i have 2 spheres, one big sphere and one small (R>r),
both are rolling from the same point down the way.

at the end of the way, which sphere would have bigger speed?

i thought the smaller sphere would have, since,
angular acceleration = (f * r ) / I = f / (0.4MR)
now if R>r shouldn't the acceleration be smaller as well?

Homework Equations

The Attempt at a Solution

 

[Delphi51]

I'm having trouble wrapping my mind around that Torque approach. It seems to me the torque would depend on the angle of the ramp in a complicated way. Still, the higher the moment of inertia, the smaller the acceleration.

It seems much clearer to me from an energy point of view. You might try beginning with
Energy at top of ramp = energy at bottom of ramp
putting in ½mv² + ½Iω² for the bottom where it has both translational and rotational kinetic energy. There is, of course, a relationship between v and ω so you can simplify to one speed variable.
I think you are missing a ² in your expression for moment of inertia. Note also that it depends on whether the sphere is solid or hollow.