Steel balls rolling down an incline

[wheelatharm]

This should be a pretty simple question for someone out there,

If you have a ramp with the same height, and the same angle, and you take two spheres of different size, but identical materials, and you rolled them down this incline. Which would reach the bottom first if rolling friction is ignored, a small diameter ball, or a large diameter ball, and what is the equation that shows why?
When I actually do this, I get the large sphere reaching the bottom first, but it is not a great difference, and I can't rule out friction.

I know that with the same potential energy, I will get a split between linear kinetic energy and rotational energy that is the same regardless of size, and when I look at the effect of size on the conservation of energy equation, all the factors that relate to size canceled out, so this is why I think that it does not matter, but I am not always great at making math connections, and I have the feeling I missed something.

Marc

 

[LightHero]

W. McCord's answer to this question is correct. The equation that explains why a large diameter ball will reach the bottom of the ramp first is as follows: F = ma, where F is the net force acting on the ball, m is the mass of the ball and a is the acceleration of the ball. Since the balls have the same potential energy, the larger ball will be accelerated more quickly due to its greater mass, giving it a greater force and therefore a greater speed. This means that the large diameter ball will reach the bottom of the ramp first.