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PROFESSOR: And I want to show that to you.
You have a setup here, and I'll try to show that to you also
on the screen there.
But for those of you who are sitting close, it's probably much better that
you just look at the demonstration right here.
I have here, to start with, a very heavy cylinder made of brass.
And this one is made of aluminum.
They have very different masses, same radii, same length.
Should make no difference.
Should be no winner.
There should be no loser.
I'm going to start them off at the same time.
I hope you can see that there.
This is the starting point to lower it a little.
I will count down three to zero, and then you can see that they reach the
bottom almost at the same time.
So very different in mass.
The mass difference is at least a factor of three.
All other dimensions are the same.
Three, two, one, zero.
Completely in unison.
Not intuitive for me.
Now I have one that has a very small radius compared to this one-- this is
a small aluminum rod.
Maybe you can see it here--
television.
This is way more heavy, almost 30 times heavier.
Should make no difference.
As long as it's solid, should make no difference.
No winner, no loser.
Radii are different.
Masses are different.
Should make no difference.
We start the race--
three, two, one, zero.
And they hit the bottom at the same time.
Now here I have a hollow one.
You better believe that it's hollow.
So now all the mass is at the circumference.
And now it takes more time.
Now the acceleration, as you will see, is 1/2 times g sine beta.
In the other case, it was 2/3.
And you may want to think about it tonight, why this one takes more.
It has to do, of course, with the moment of inertia.
But again, it's independent of mass, radius, and length.
So it's purely a matter of geometry.
This one is going to be the loser, and this one-- regardless of mass or
length-- is going to be the winner.
So you see them.
One is hollow.
One is not.
This is very light.
This is very heavy.
I'll put the hollow one on your side.
Three, two, one, zero.
The hollow one lost and even fell on the floor.