Moment of inertia rolling down a hill

AI Thread Summary
When rolling down a hill, both a large, massive sphere and a small sphere with low mass reach the bottom simultaneously due to the physics of rolling without slipping. The moment of inertia for solid spheres is given by the formula ICM = (2/5)MR², but in this scenario, the mass and radius cancel out in the equations of motion. The discussion highlights the importance of understanding the forces acting on the spheres and the relationship between linear and angular velocities. Despite initial assumptions that the larger sphere would win due to its mass, the outcome remains the same for both spheres. Proper mathematical analysis confirms that they reach the bottom at the same time.
lo31415926535
Messages
18
Reaction score
0

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



ICM= (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?
 
Physics news on Phys.org
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?
 
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.
 
Just gravity is acting on them right? So the larger, more massive one would reach the bottom first?
 
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.
 
Last edited by a moderator:
okay so since the masses and radii drop out, they reach the bottom at the same time?
 
why would the masses and the radii "drop out" - did you do any math?
 
that's what it was on your second example… What math am I supposed to do??
 
Have you had a look at the links I have given you?
 

Similar threads

Moment of Inertia with pulley and two masses on a string (iWTSE.org)
Replies
8
Views
12K
Distance rolled of sphere vs cylinder with same m, r, and v
Replies
5
Views
700
Deriving the moment of inertia of a sphere
Replies
6
Views
2K
Wooden sphere rolling on a double metal track
2
Replies
97
Views
5K
Effect of density on downward rolling spheres
Replies
14
Views
4K
Objects with Different Moments of Inertia Rolling Down an Inclined Plane
Replies
5
Views
2K
Identical Hollow and Solid Spheres
Replies
4
Views
7K
Rolling without slipping problem
Replies
42
Views
3K
Moment of inertia for this assembly
Replies
2
Views
7K
Moment of Inertia of Solid Sphere - Proof
Replies
3
Views
5K

Hot Threads

Recent Insights

Back
Top