AP Physics: All objects are placed at the top of a smooth incline and started simultaneously (symmetry axis) . In what order do they cross the finish line- and why?

Question

Consider a race between the following objects:

1. A: playground ball (hollow, heavy rubber ball aka sphere)
2. B: lacrosse ball (small, solid rubber ball)
3. C: segment of cylindrical metal lab pole-- aka long disk
4. D: embroidery hoop (wood ring)
5. E: sanitary sewer- cover (large, solid metal disk)

All objects are placed at the top of a smooth incline and started simultaneously (symmetry axis) . In what order do they cross the finish line- and why?

question 1:

All objects are placed at the top of a smooth incline and started simultaneously. In what order do they cross the finish line? Put the letters A-E into the order in which the objects would finish the race, if there is a tie then put the tying letters into alphabetical order so for example:

x-2nd      y - tie for 4th       q  - 3rd          r -tie for 4th       s-wins

The order would be: 1- s, 2- x, 3- q, 4- r, 5- y

r and y tied by r comes first in the alphabet so it got listed first

question 2: Explain your reasoning for the ranking- what do you look at to determine the order in which the objects will finish? Why is this the determining factor?

Answer 1

Hi Sumin K.,

All your work has been done for you! The motive force is always ∼ Mg, but the "resistance", i.e. development of angular momentum, which imparts also rotational kinetic energy! -- varies among the object geometries. So classify your objects, then rank them:

B is a solid sphere with 2/5 MR^2 "resistance", next are C and E, both essentially discs at 1/2 MR^2, next A at 2/3 MR^2, and last D at MR^2. These are ranked in order of increasing "resistance to rolling", in the same way that F=m*a uses m as the "resistive" element to regulate the action of F on a ! So, B rolls fastest. However, I'd like to point out that a hollow ball filled with a non-viscous liquid would beat them all, since it maximizes motive force whilst minimizing angular momentum gain. In fact, I once made some filled ping-pong balls to demonstrate just that, for some inner-city high-schooler science classes -- they lasted about ten minutes before the students had destroyed them.