A ring and a disk of equal mass and radii have a race rolling down an incline
of height 
and length 
.
Which wins? We'll work this out in detail using energy conservation.
The total 
at the bottom for each is, of course, 
.
We'll calculate the velocity of each at the bottom.
For the ring:
So
For the disk:
So
.
The disk has a greater velocity at the bottom, and therefore wins the race! Note that the time each takes is
