Julius Sumner Miller: Lesson 12 - The Strange Behavior of Rolling Things

When we roll things down an inclined plane we discover a strange business: The mass of the rolling body does not matter. What matters is how the mass is distributed. To explore these wonderful thing we roll disks and hoops and spheres - all sizes - all masses and very enchanting discoveries are made.

A - We first roll a solid disk and a hoop. They have the same diameter -
the same mass - the same weight. How do they roll? That is - do they roll together? Does the disk win? Does the hoop win? We discover that the disk beats the hoop.

B - Now we roll an array of disks and hoops. And what do we find? We find that ALL disks roll alike. We find that ALL hoops roll alike. AND - we find that every disk beats every hoop. Little disks - big disks - fat disks - skinny disks - ALL DISKS BEAT ALL HOOPS. Now -how can I say this? One cannot roll ALL the disks and all the hoops in the whole WoTId! ANSWER: The MATHEMATICS tells us all this in a jiffy:
FR = lot and Mgh = 1/2 MV + 1/2 \(n . So you see how very much a brief sentence in mathematics can tell us.

C - We further find that ALL SPHERES ROLL ALIKE. Little spheres - big spheres - tiny spheres - ALL SPHERES - roll alike. But they must be solid uniform spheres like steel balls.

D - Now the question: Suppose we roll disks and spheres and hoops? What now? And to sum up our wonderful discoveries we say:
1 - All disks roll alike
2 - All hoops roll alike
3 - All spheres roll alike
4 - All spheres beat all disks
5 - All disks beat all hoops.
This is really wonderful to know.

E - The bodies we have rolled are very special. They are uniform in their mass distribution. So - we ask: what happens if the bodies are \