Two balls same radius and mass rolling down a slope

[Nina87]

two balls, one made of iron and one made of lead with same radius and mass. which one will roll down the slope faster?

i don't really know where to begin, since everything is the same, the only idea i had was to somehow relate Ek=(J.ω2)/2 => Ek= m.r2.(ω2/2) to the question since i imagine that for them to r1=r2, m1=m2 one must have thinner wall. but then i can't isolate 'v' from the equation to actually prove something.

 

[gneill]

two balls, one made of iron and one made of lead with same radius and mass. which one will roll down the slope faster?

i don't really know where to begin, since everything is the same, the only idea i had was to somehow relate Ek=(J.ω2)/2 => Ek= m.r2.(ω2/2) to the question since i imagine that for them to r1=r2, m1=m2 one must have thinner wall. but then i can't isolate 'v' from the equation to actually prove something.

Hi Nina87, Welcome to Physics Forums.

I think that you're thinking along the right lines. First determine which of two spheres with equal radii and mass but different moments of inertia will roll faster. You don't need any particular numbers to do this, just see how the acceleration or velocity depends upon the moment of inertia.

With that established, pick a method for making your lead ball of equal mass to the iron one. One way would be to hollow out a small sphere of appropriate mass from the center of the lead sphere. What would be the moment of inertia of the result? Larger or smaller than that of the solid iron sphere?

 

[Nina87]

hi, thanks for your help.
so as i understand with increasing radius increases moment of inertia.the moment of inertia of an object is a measure of how difficult it is to start it spinning. and as i imagine it,some parts of the iron ball are closer to the axis, therefore it has smaller moment of inertia (J=m.r2) compared to the lead ball(the task doesn't specify that one is solid and another is not).
i still don't know how velocity depends upon moment of inertia but my best guess is that since both balls are of equal mass they have equal potential energy. Ep= - Ek; Ek= (J.ω2)/2 so then it follows that their J & ω are different. assuming that the iron ball has smaller moment of inertia, it's ω must be bigger than the one of the lead ball.
v=r.ω (radii are equal; velocity of the iron ball is bigger).