Mr.p: Good morning.
The center of mass of an object is the mass-weighted average position of all the mass of the object.
For an object with constant density and symmetrical shape like this lacrosse ball,
the center of mass is directly in the center of the object.
Bobby: Sure.
Bo: That makes sense.
Billy: The center of mass of a constant density sphere is directly in its center.
"Flipping Physics" Intro
Mr.p: You can see the shape of the path created by the ball moving in projectile motion is a parabola.
We have talked about this before but what you might not have realized
is that we have been specifically talking about the motion of the center of mass of the ball.
Watch what happens when we add a hammer moving in projectile motion.
The motion of the hammer seems to be much more complicated.
However, realize that the hammer rotates around its center of mass
and the motion of the center of mass of the hammer still follows a parabola just like the ball.
In other words, we can treat the hammer as if all its mass were located at the center of mass
and consider the force of gravity to be acting at that center of mass, just like it does for the ball.
Billy: Uh, Mr. P? I'm a little confused. Are we talking about center of mass or center of gravity?
Mr.p: Oh yeah, right, thanks Billy.
As long as the object is in a constant gravitational field,
the center of mass center of gravity of an object are in the same location.
Here on planet Earth, the acceleration due to gravity is nearly constant;
therefore, we generally consider center of mass and center of gravity to be in the same location.
But it is worth noting that this is only true when the gravitational field is constant.
Okay, let's add some more objects moving in projectile motion:
a baseball bat
a bone
an Einstein action figure
an adjustable wrench
a hoop Frisbee
a turtle
Again, notice the center of mass of all of these objects follows the parabolic path
of an object in projectile motion
and we can treat each object as if the force of gravity acts on the object's center of mass.
This is true for all objects in projectile motion. Even me jumping the wake on a wakeboard.
Bo: Nice.
Billy: That looks like fun, Mr. P.
Bobby: Hold up a second, um, can you go back to the Frisbee ring for a minute?
That means the center of mass of the Frisbee ring is not actually located on the object, right?
Mr.p: That's a good point, Bobby.
Realize the center of mass of an object is not necessarily located on the object.
As you pointed out for the Frisbee ring, it is located in the geometric center, which is not actually on the ring.
I do want to point out that all of these examples are actually being shown at a speed
32 times slower than reality, because when we look at them at real speed like this,
it happens way too fast to understand what is happening.
BBB: Thank you Mr.p! Cool. Sure.
Mr.p: I should also point out this works for systems of objects as well.
For example, we can have three balls all moving in projectile motion.
The center of mass of the system of those three balls still follows the same projectile motion path.
Because, even though those balls are all moving relative to one another, they still have a center of mass
which moves in a parabola in projectile motion just like all the other objects we demonstrated.
Okay, it is also typical to talk about the center of mass of two objects connected by a thin rod.
these two ice cubes are connected by a thin rod
and the center of mass of the system is indicated by the black dot.
When I apply a force on the rod to the left of the center of mass of a system,
the applied force rotates the system.
When I apply a force on the rod to the right of the center of mass of the system,
the applied force rotates the system in the other direction.
And then, when I apply a force on the rod at, or directly toward, the center of mass of the system,
the system does not rotate.
In other words, if you apply a force to an object at, or directly toward, its center of mass,
the force applied will not cause the object to rotationally accelerate,
the force will only cause a linear acceleration of the object.
Another fun example of center of mass is a Weeble,
which is an egg-shaped toy, which always returns to an upright position.
A normal egg placed on its end will fall over.
However, this toy I made stands on its end.
The way I made the toy was by hot gluing a large mass into the bottom of the plastic egg.
What that does is, it moves the center of mass of the egg so it is very near the bottom of the egg.
The lowest black dot on the egg is a good approximation of the center of mass of the toy egg.
As it is tipped over, the center of mass of the egg actually goes up.
The force of gravity pulls down on the center of mass of the egg such that when I let go of the egg,
the center of mass is pulled downward and the center of mass goes to its lowest position.
This looks strange to us because we tend to assume the centers of mass of objects are located near the
geometric centers of the objects, however, that clearly is not always the case.
Billy: That looks like fun. I gotta make one.
Bo: Of course.
Mr.p: This brings us to a simple way to find the center of mass of a flat object.
For example, this irregularly shaped flat piece of wood.
When we hang the wood,
the force of gravity pulls on the center of mass of the wood to bring the center of mass to its lowest point,
just like it did on the toy egg.
That means the center of mass of the irregularly shaped piece of wood
must be below the point where it is hanging from.
If we draw a vertical line there, the center of mass must be along that line.
We can then rehang the wood from a different point and again draw a vertical line from the hanging point.
The intersection of those two lines must be where the center of mass of the wood is.
We can then add this symbol at the center of mass of the block
because it is the symbol which is typically used to indicate the center of mass of an object.
Bo: And then throw it.
Bobby: Because it will rotate around its center of mass.
Billy: And the center of mass of the irregularly shaped piece of wood will follow a parabola
because the wood is in projectile motion. That's cool!
Mr.p: Very nice observations everybody. That is my center of mass introduction.
Thank you very much for learning with me today. I enjoyed learning with you.