Basic science question...

[mrd]

I just meant 3-D in terms of basic shape. As in, it can roll properly on any point. A ring or coin on the other hand can only roll in the plane of the circumference. I'm thinking of when you roll a coin and it abruptly changes direction.
But like I said, that's really grasping at straws and probably isn't the real explanation.

That's too much of a real world application. I think TB is leaning more towards "perfect" theoretical situations.

[Guest]

No, you're all wrong. I'll give you a huge, massical hint.

Torque = what? * angular acceleration

[[xeno]Julios]

not really familiar with angular accel and torque and the like, but it's unclear to me that the sphere would reach the bottom first for reasons other than friction.

[werldhed]

Yeah, I don't see how torque comes into play here. If they have the same mass and radius, shouldn't torque be the same?

[mrd]

Torque is angular accel * distance from the pivot to where the force is applied, no?

If everything has the same radius, then they have all the same pivot point, so they all have the same distance from the pivot to where force is applied.

[tnf]

look at it in terms of forces and acceleration only. If all 3 were in freefall, ignoring air resistance, the only force acting on them is gravity. Regardless of mass, all 3 will fall at the same rate, because the net force on them is due only to gravity.

Now, throw them all on ramp, the only force on them is gravity - and the acceleration will still be equal in all 3 cases.

So where does torque come into play?
Torque applied to forces tangentiel to the circle if I remember correctly...

[tnf]

and I think you need moments of inertia for that too...

*google check*

yup, it looks like it.

but maybe not.

[[xeno]Julios]

toxic - here's a question.

did you make this puzzle up, or did you get it from a source?

[Nightshade]

If there is friction, which I think we've established there IS in this problem, and all objects have the same circumfrence...
I believe it will be the sphere, which has the smallest surface area in contact with the slope.

you're right but your explanation is completely off.

Here's a question, if you have a perfectly spherical object resting on a perfectly flat surface, how much of the sphere is in contact with the surface?

An infinitesimally small point.

[werldhed]

I was going to mention inertia, but if they all have the same mass... then... nothing...

[tnf]

you're right but your explanation is completely off.

Here's a question, if you have a perfectly spherical object resting on a perfectly flat surface, how much of the sphere is in contact with the surface?

An infinitesimally small point.

yea, because basically the ground and the point of contact would be like a tangent line intersecting a circle at just one point...right?

[[xeno]Julios]

so mathematically 1/infinity right?

[Guest]

Ok, here is the explanation. I don't know what they teach you in the US or wherever you've done your education, I don't know if any of you are mechanical engineers, but I am sure one would get an answer to this problem extremely easily.

Torque = (moment of inertia) * (angular acceleration)

The friction on the hill and the gravity apply a constant torque on all the ring, the sphere, and the coin. Therefore the torque is the same for all three. So what interests us is the angular acceleration, since the faster the objects accelerate, the faster they will roll, thus the faster they will reach the bottom of the hill.

(Angular accleration) = (Torque) / (moment of inertia)

Therefore the object with the smallest moment of inertia will reach the bottom of the hill quicker.

The moments of inertia for the three objects are the following:

moment of inertia of a ring = MR²
coin = (1/2)MR²
sphere = (2/5)MR²

Therefore the sphere has the smallest moment of inertia, considering they all have same mass and radius. Therefore the sphere will be the first one to reach the bottom.

[werldhed]

Fair enough, but where do those equations come from? Why does a sphere have a smaller moment of inertia?

[mrd]

Yeah. And why do the coins and rings have different MOI?

[Guest]

Fair enough, but where do those equations come from? Why does a sphere have a smaller moment of inertia?

Google it, there are specific formulas for deriving the moments of inertia of different objects. Its all math, you might have fun with it.

[[xeno]Julios]

i'm guessing it's coz the moment of inertia is around the plane that's parallel to the roll of the sphere, and the sphere has the least amount of mass distributed around this plane compared to the ring and coin which has all of its mass distibuted about this plane.

[mrd]

Here's a link for the MOI of a sphere, indeed it is (2/5)MR squared. Kinky.

http://hyperphysics.phy-astr.gsu.edu/hb ... .html#sph2

[Guest]

Btw, moments of inertia:

http://oak.cats.ohiou.edu/~piccard/phys251/moments.html

http://www.physics.uoguelph.ca/tutorial ... ertia.html

[Guest]

By the way, I really think that you need to be in mechanical engineering to do this sort of physics, since its not in any of the obligatory science courses at my school, I'm taking a "Physics For Engineers" optional course (gotta take 3 optional courses) and because of this course I've decided not to go into engineering in university

[werldhed]

Fair enough, but where do those equations come from? Why does a sphere have a smaller moment of inertia?

Google it, there are specific formulas for deriving the moments of inertia of different objects. Its all math, you might have fun with it.

Probably not. I'm no physicist. In fact, I just remembered why I'm online in the first place. I was trying to answer my own science questions:
-Describe a culture-independent method of identifying an organism.
-How would you go about identifying all the genes in an organism that interact with an environmental stimulus using a functional genomics approach?

oops. Damn your distractions! I should probably do that.

[Guest]

Heh, I'm guessing that tnf would answer these quite easily. I know nothing about biology and I'm afraid of the bio class I have to take in orde r to get my diploma

[Nightshade]

Here's a question, if you have a perfectly spherical object resting on a perfectly flat surface, how much of the sphere is in contact with the surface?

An infinitesimally small point.

yea, because basically the ground and the point of contact would be like a tangent line intersecting a circle at just one point...right?

The ground is a plane tangent to the sphere, which, by definition, only touches the sphere at a point.

[Nightshade]

so mathematically 1/infinity right?

Errm, well, technically if you evaluate the limit of 1/x as x goes to infinity, it's zero, but I don't see the direct connection to the sphere/ground issue.

[Nightshade]

By the way, I really think that you need to be in mechanical engineering to do this sort of physics, since its not in any of the obligatory science courses at my school, I'm taking a "Physics For Engineers" optional course (gotta take 3 optional courses) and because of this course I've decided not to go into engineering in university

No, you don't need to be in an ME program. That material is covered in a first semester physics course.