Two objects of identical mass, one is a cylinder, the other a sphere, (same diameter)set to roll down a slope. Ignoring friction and wind resistance, which reaches the bottom first?
Unfortunately I don’t remember which college student posed the problem, so I need to post it for the general public. I know MY answer, but I would be interested to get an official physics-type to verify.
Thanks,
T
If you’re ignoring all factors other than mass, there are two answers:
both
neither
As I recall, you can ignore mass too. Objects will accelerate at the same rate regardless of mass provided you remove friction etc from the picture.
May I ask what prompted the question?
And if you’re not ignoring all other factors…ie, a real-life environment with all the oddities that may befall the rolling objects…then the sphere will be less impeded by the possibility of getting directionally skewed and losing momentum.
If you’re ignoring friction, then they’re not rolling, they’re sliding, in which the case is they arrive at the same time.
If they’re rolling, the sphere will accelerate faster. Its moment of inertia (the equivalent of mass for rotational motion) is 2/5 mr^2, whereas that of the cylinder is 1/2 mr^2, where m is the mass and r the radius.
Hey! I recognize this problem! Sounds rather too much like a physics problem I was doing while working on homework in chat one night… 
The professor later posted the answer on the web, this is his reply:
Q16. The sphere has greater speed at the bottom and reaches the bottom first. The total KE at the bottom = PE at the top = Mgh, which is the same for both, since both have the same mass. The sphere has a smaller moment of inertia I than the cylinder. Since, rotational KE= ½Iω2, the cylinder will have the greater rotational KE and the smaller translational KE, which is why the sphere win the race.
What ever happened to 2+2??
Thanks, Karina! I was wrong too. . .but at least I know the answer now!