It's already pretty obvious that the mallet is following the arc of a falling
object as it's rotating. But just to make that crystal clear.
I'm going to show you the same throw again, one-tenth its original speed, with
all the images of the mallet lingering on the screen, but this time I am going show
the arc of a falling object that travels along in the path taken by the mallet's
center of mass[BLANK_AUDIO][SOUND]. So you see, when you throw something, and
it becomes a falling object. That is, it's experiencing only one force,
its weight. Its motion is actually fairly simple.
The object's center of mass travels in the arc of a falling object.
As though it were a simple thing like a falling ball.
At the same time, the rest of the object may be rotating about that center of mass.
The object's natural pivot. So the object is doing two things at once.
It's translating in the arc of a falling object as it's rotating in the manner of
an object that's just simply free to rotate about its own natural pivot.
Its center of mass. This may look like an ordinary beach ball,
but it's not. Watch how it moves.
It's hard to catch. [laugh] Why does this beach ball move in
such a crazy manner? This beach ball has its center of mass
located far from its geometrical center. There's a container over here on the side
of the beach ball that's full of water so that the most, most of the mass of the
ball is located here where I can touch. As a result, the center of mass is here on
the surface of the ball. And when I throw the ball, and it becomes
a falling object, it's that center of mass that travels in the arc of a falling
object. The rest of the ball comes along for the
ride. And it rotates about its center of mass,
it's natural pivot. And therefore about one surface, one side
of the ball. So that wobbly motion you're seeing is the
ball rotating about the side of the ball, it's natural pivot where the center of
mass is located. You can begin to locate a small object's
center of mass by setting it on a surface to support it's weight and then giving it
a spin. It naturally spins about it's center of
mass. So, what I can say in, for this basketball
is that the center of mass of the basketball lies somewhere on this
rotational axis. It's spinning about a line, passing from
top to bottom of the ball, and the center of mass is located on that line.
I can't tell you for sure where along that line is unless I rotate the ball and spin
it again, rotate the ball and spin it again, but eventually, I could pin down
the fact that for a basketball, the center of mass is pretty much dead center in the
geometrical center. That's true of a basketball.
But not so true for knife. How do you find the center of mass of a
knife? Give it a spin.
It's right about there. It's somewhere, that's the point that's
staying put as it spins. It's spinning about that point.
So I can tell you the center of mass is somewhere ...between my two fingers.
To pin it down further, I'd have to spin the knife about another axis.
Can I do it? Ooh.
I can. So now I've really pinned down the center
of mass of the knife. It's really right there in the middle of
this metal piece. Well, for a seesaw, you do the same thing.
So here's a seesaw board. You give it a spin.
The point that's trying to stay put is right about here.
So that's, that's the center of mass. Somewhere between my fingers.
And that's where the pivot goes when you make the seesaw into a real rideable
seesaw. And I can pull one of those up.
Here it is. The rideable seesaw if you're very, very
small. Is supported right at its center of mass,
and therefore pivots naturally about that point.
So we're supporting it right at its center of mass, and allowing it to undergo
rotational motion about its own natural pivot.
When examining rotational motion, it's technically necessary to specifiy the
center of rotation. That is, the point about which all the
physical quantitites of rotational motion are defined.
We're free to choose that center of rotation.
But some choices are better than others. For example, if I'm rotating like this and
we want to describe my rotation as simply as possible using the physical quantities
of rotational motion, the most obvious choice for a center of rotation about
which to build our language is my center of mass, 'cause that's the point about
which I'm pivoting. So, in this case, we define the center of
rotation as located at my center of mass. So for example, my angle of velocity now
is about 90 degrees per second up, remember the right hand rule, about my
center of mass. So about my center of mass, is pinning
down the center of rotation about which our language is built.
But if I'm rotating not about my center of mass, but about my thumb, watch this.
Here we go. I can pivot about things other than my
center of mass. I need help to do that.
But I can do it, and I'm now pivoting about my thumb.
So, it makes good sense to define that as our center of rotation and to say that I
am currently rotating. My angular velocity is about 90 degrees
again, up, about my thumb. That's the center of rotation.
Well By now I hope you can see that while choosing a center of rotation is necessary
to define the physical quantities of rotational motion, stating that center of
rotation explicitly every time you use 1 of those physical quantities is, is a
nuisance, and I'm going to stop doing it. Instead I'm going to assume that the
center rotation that we have in mind is obvious, unless it's not, in which case I
will say it. So, for this case of a seesaw mounted with
a pivot passing right through its center mass, its own natural pivot, that is an
obvious choice. For our center of rotation.
Right here in the middle of the board where the pivot passes through the center
of that board. The board's center mass.
That's the obvious choice for the center of rotation.
And it will assume for the remainder of this story, that every physical quantity
of rotation is defined about that point. So, instead of adding language now to all
our physical quantities of rotation for the seesaw.
Let's put some riders on it. And that's the job for the next video.
