Moment of inertia rolling down a hill

[lo31415926535]

Homework Statement

Two solid spheres -- a large, massive sphere and a small sphere with low mass -- are rolled down a hill. Which one reaches the bottom of the hill first?

Homework Equations

I_CM= (2/5)MR²

The Attempt at a Solution

I thought that this would be the smaller sphere because it has a lower moment of inertia… but this isn't right. Can someone please explain?

 

[Simon Bridge]

You have to do the physics ... what are the forces on the cylinders and the constraints?
Have you just done a lesson or so on rolling without slipping?

 

[lo31415926535]

What physics do I have to do? My teacher talked about it a little… but honestly he is not very good at explaining things so I am having trouble understanding this.

 

[lo31415926535]

Just gravity is acting on them right? So the larger, more massive one would reach the bottom first?

 

[Simon Bridge]

The wheel has to roll as well - so it will have an angular velocity.
Have a look at how other's do it.
http://faculty.wwu.edu/vawter/PhysicsNet/Topics/RotationalKinematics/RollingWithoutSlipping.html
https://www.physicsforums.com/showthread.php?t=169313
... there are also video tutorials on youtube.

 

[lo31415926535]

okay so since the masses and radii drop out, they reach the bottom at the same time?

 

[Simon Bridge]

why would the masses and the radii "drop out" - did you do any math?

 

[lo31415926535]

that's what it was on your second example… What math am I supposed to do??

 

[Simon Bridge]

Have you had a look at the links I have given you?