spheres and discs and hoops

[billy rubin]

folks, i have a question

years and years ago . lots of years ago. i was maybe ten years old, so dinozaurs still roamed the earth, or so my kids tell me.

anyway, i read about a physics teacher who taught physics through demonstration. one of his demonstrations was to set up a long inclined plane and then roll thingz down it. he rolled a sphere. a disc. and a hoop, and took bets from his students as to which would get to the bottom first.

at the end, he concluded, spherez roll faster than discs, which roll fazter than hoops.

is thistrue? what mechanizms are involved? are there exceptions? what sorts of things make uze of thiz principle, if anything?

ive wondered about thiz since, well, since dinosaurs roamed the earth . . .

[No one]

Q: What can a woman put in her hoop earrings to make her more attractive?


A: Her ankles.


Thank you. Thank you.
I'll be here all week, try the salmon.

[billy rubin]

nobody told me when i got here that this place was designed by salvador dali

[No one]

Then how did you get in?

[billy rubin]

[No one]

You look nice in blue.

[Tank]

If the three objects had the same mass and diameter he was correct.

[Magdalena]

Q: What can a woman put in her hoop earrings to make her more attractive?


A: Her ankles.


Thank you. Thank you.
I'll be here all week, try the salmon.

You're so funny.
Thank you.
Yes.
OK.

[billy rubin]

If the three objects had the same mass and diameter he was correct.

well, what's the reason? they would all have the same center of gravity.

the hoop would have its mass concentrated at the rim, the disc would be uniform, and the sphere would have it concentrated towards the center, looking at them from the side in 2D

oh wait

it's angular momentum, isn't it?

a sphere of the same diameter and mss as a hoop has most of its wieght concentrated towards the center, while a hoop has it on the circumference. and the disc is in the mioddle

[Dark Lightning]

In the first video, as with the last, the rate of rotation is related to the moment of inertia. Angular momentum is the result of the distribution of mass, not the reason for the varying rates of acceleration.

[Icarus]

I believe that out Italian friend Galileo demonstrated this phenomena a very long time ago.   The weight of the object has no influence on the rate of acceleration. If aerodynamic resistance plays into the experiment then there could possibly be some differences in rate of acceleration. Aero resistance is a function of velocity squared.  A short inclined plane would not yield much observable difference in the final velocity....or time to arrive at the end of the ramp.  A longer ramp that could allow the velocity to increase, exponentially, would let the objects come under the influence of meaningful aero drag.   

The object with the largest frontal area would not necessarily be the loser of the race.  All that would depend on the coefficient of drag of the object.   Without benefit of actual experiment I would wager that the hoop might be the loser of the race down a long inclined plane.

[hermes2015]

I believe that out Italian friend Galileo demonstrated this phenomena a very long time ago.   The weight of the object has no influence on the rate of acceleration. If aerodynamic resistance plays into the experiment then there could possibly be some differences in rate of acceleration. Aero resistance is a function of velocity squared.  A short inclined plane would not yield much observable difference in the final velocity....or time to arrive at the end of the ramp.  A longer ramp that could allow the velocity to increase, exponentially, would let the objects come under the influence of meaningful aero drag.   

The object with the largest frontal area would not necessarily be the loser of the race.  All that would depend on the coefficient of drag of the object.   Without benefit of actual experiment I would wager that the hoop might be the loser of the race down a long inclined plane.

I'm pretty sure someone has tested this in a vacuum chamber.

[billy rubin]

back in school i took physics for poets

moment of inertia is buried deeply. i will go do some digging.

[Ecurb Noselrub]

What about the role of friction? If one object has less area in contact with the surface it has less friction slowing it down.

[Dark Lightning]

If an object is rolling, the friction is going to be minuscule, and dependent on the surface finishes of the incline and the objects- like if the surface is bumpy on a scale that affects the rolling. The only role friction actually plays when these objects roll, is that that they roll instead of sliding.