- Good morning.
Billy, what is the form of Newton's second law
which does not include momentum?
♫ Flipping Physics ♫
- Okay, that is net force equals mass times acceleration
where both force and acceleration are vectors.
- Correct.
Now, previously we showed that an object
moving along a curved path
must have a centripetal acceleration.
Bobby, what is the direction of centripetal acceleration?
- Centripetal means center seeking
so centripetal acceleration is inward.
- Therefore, when an object is moving along an arc,
in addition to having a centripetal acceleration,
according to Newton's second law,
it must also have a centripetal force.
And that centripetal force is the center-seeking net force
in the inward direction.
This net force in the in direction, this centripetal force
is what causes circular motion.
Now, there are three things I need you
to remember about centripetal force.
Centripetal force is not a new force.
In order to understand what I mean by this,
understand that all the other forces
we have introduced before,
force of gravity, force of tension,
force of friction, and force normal,
these are all independently defined forces.
However, centripetal force is not a new,
independently-defined force.
It is the net force in the in direction,
which means it is made up of those other forces.
It might be just one of them,
or it could be a combination of those forces.
In other words, the centripetal force
could be the force of gravity.
It could be the force of tension,
it could be the force of friction,
it could be the force normal,
or it could be a mixture of those,
because it is the net force in the in direction,
the sum of the forces in the in direction.
Centripetal force is not a new force.
Because centripetal force is not a new force,
it is never in a free body diagram.
In order to determine what the centripetal force is,
you first draw your free body diagram,
and then you sum the forces in the in direction.
That net force in the in direction is the centripetal force.
Lastly, when summing the forces in the in direction,
the in direction is positive,
and the out direction is negative.
In is positive, and out is negative.
Let's take a moment to look at one mint on a turntable.
Bo, please draw the free body diagram
of all the forces acting on the mint,
which is revolving around the center of the turntable.
- [Bo] Uh, could you please pause the record player
so I can draw the free body diagram?
- [mr.p] Absolutely, and I'm glad you recognize
it is generally easier to draw a free body diagram
at a specific point in time.
So yes, I will pause the video,
however, realize the mint is not stationary.
It is moving in a circle at this moment.
Also, I will add a side view of the mint
to make it easier to draw all the forces.
- [Bo] Okay, the force of gravity is down.
The force normal is up,
and the force of static friction is in toward the center.
- [mr.p] Correct.
Now, look at what happens when I set the top view
in motion again.
The force of static friction is always inward.
And when we pause the video with the mint on the left,
we can add that side view as well
along with its free body diagram.
Actually, for clarity's sake,
let's remove every force but the force of static friction
from the free body diagrams.
Now, notice, when the mint is on the left,
the force of static friction points rightward and inward,
and when the mint is on the right,
the force of static friction points leftward and inward.
If we were to sum the forces in the x direction,
this would be confusing
because the direction of the force of friction
would be changing.
In other words, when the mint is on the right,
the net force in the x direction would equal
the negative force of static friction.
However, when the mint is on the left,
the net force in the x direction would equal
the positive force of static friction.
This is unworkable, which is why we sum the forces
in the in direction.
And the force of static friction in this example
is always in the in direction.
The net force in the in direction in this example
always equals the positive force of static friction.
So for the mint, in this specific example,
the net force in the in direction or the centripetal force
is the force of static friction.
That is what it means,
that the centripetal force is not a new force.
That is just one example,
but don't worry.
We will analyze many more situations
where we draw the free body diagram
and sum the forces in the in direction
to determine the centripetal force.
Thank you very much for learning with me today.
I enjoyed learning with you.