Hi. It’s Mr. Andersen and this is AP Physics essentials video 58. It is on motion of the
center of mass. And one of my favorite toys when I was really young were Weebles. And
what you could do is you could push on it like this and what they would do is they would
wobble back. The saying went that “Weebles wobble but they don’t fall down.” And
so what is the physics behind that? Well you have to understand what the center of mass
is. If you look at a Weeble it is an egg shape, but the bottom has a huge amount of density.
And so the center of mass or this mean center of the object is really really low. If it
was high, the center of mass, it would simply fall over. But when you would push on it,
what you would do is you would take it out of equilibrium. You can see the center of
mass would raise a little bit and then it would just wobble back to where it was. Another
fun thing to do with Weebles was to throw them or spin them in the air and they would
do this kind of looping action. And that is because they are revolving around that center
of mass. And so when you are measuring linear motion or change over time what you really
have to do with an object is find its center of mass. And that is going to be the mean
position of the matter. So it is the average position of the matter. It is going to be
right on the inside. And so if we really want to measure the linear motion of this object,
let’s put it in motion, what we can do is figure out where that center of mass was at
the beginning, where it is at the end and that would give us its displacement. Remember
if we divide that by time it would give us its velocity. And if we give that over time
that is going to give us our acceleration. And so an example of this is if you have ever
thrown a hammer you get this weird kind of an action. So I am going to throw this hammer
across the screen and just watch it carefully. And you can see it is just kind of moving,
it seems like a random motion across the screen. An ax would fall with a similar kind of a
path. And so what is going on here? Well if we figure out where the center of mass of
the hammer is, since it is really heavy at the top, the center of mass is going to be
closer toward the top. And what we are going to do now is let’s eliminate the hammer,
it is still there but you can not see it as well. I have marked the center of gravity.
And now I am going to do the same thing. I am going to throw it across the screen and
watch what happens. You can see that that center of mass, I have slowed it down a little
bit, is right along that line. And so if we can figure out where the center of mass is
then we can accurately describe the motion of an object. And so if we had a bicycle like
this, the center of mass of the bicycle itself might be fright here. And so if we are solving
a physics problem where we treat this bicycle as one object, it is important for us to know
where that center of mass is. Because there is going to be a lot of internal forces, maybe
you are pushing on the road, you are pushing on the pedal, you are pulling back on the
handlebar, remember since we are treating this as one object, these are all action reaction
pairs. And they are going to be balancing pairs as well. And so we can simply forget
all those internal forces if we know where the center of mass is, we can just measure
the external forces acting on it and then we can figure out the linear motion of an
object. So how do you figure out the center of mass? Well it is pretty easy. If we were
to take an object like this that is uniform in density throughout, it would be right in
the center of a sphere or a cube or a cylinder. Let’s say we had two spheres. Where would
the center of mass be? It is going to be right in the middle. So it is going to be right
between the two. But let’s say we have an irregular object, how do we figure out where
the center of mass is if we do not have a formula to figure it out? Well here is a hang
test that works real well. So let’s say we have a piece of metal, it is cut like a
house like this. What we could do is we could hang it like that, so it we hang it vertically,
and then we just draw a dotted line that shows us where verticality is. And so you could
just drop a piece of string and then just kind of trace along there. We could then hang
it from another position, we could do the same thing and where those intersect, that
is going to be our center of mass. So it is the center of that material, the center of
that product itself. And so if I want to measure linear motion of an object, what I could do
is I could measure where is the center of mass to begin with. I could move it, so in
this case we are moving it for 3 seconds. Let’s say it move 12 meters. My velocity
is going to be 4 meters per second, assuming that it is moving at the same rate that whole
time. But now let’s say we do it again but it
rotates. So let’s say it is rotating around that center of mass, how do I figure out its
velocity now? Same way. I am going to take that 12 meters divided by seconds, so it is
going to be 4 meters per second. And so did you learn to use representations of the center
of mass to measure linear motion? I hope so. And I hope that was helpful.