Let's say we observe some object--
let's say for the sake of argument, it's happening in space
It's traveling in a circular path with
the magnitude of its velocity being constant
Let me draw its velocity vector
The length of this arrow is the magnitude of the velocity
I want to be clear. In order for it to be traveling in the circular path
the direction of its velocity needs to be changing
So this time the velocity vector might look like that
After a few seconds the velocity vector might look like this
After another few seconds the velocity vector might look like this
I'm just sampling. I actually could've sampled after a less time and it would be right over there
but I am just sampling sometimes as it travels around the circle
After a few more seconds the velocity vector might look something like that
I want to think about what needs to happen
what kind of force would have to act
in particular the direction of the force would have to act on this object
in order for the velocity vector to change like that?
This remind ourselves if there was no force acting on this body
this comes straight from Newton's 1st Law of motion
then the velocity would not change
neither the magnitude nor the direction of the velocity will change
If there were no force acting on the subject
it would just continue going on in the direction it was going
it wouldn't curve; it wouldn't turn; the direction of its velocity wasn't changing
Let's think about what the direction of that force would have to be
and to do that, I'm gonna copy and paste these velocity vectors and keep
track of what the direction of the change in velocity has to be
Copy and paste that
So that is our first velocity vector
Copy all of these. This is our second one right over here
Copy and paste it
I'm just looking at it from the object's point of view
how does the velocity vector change from each of these points in time to the next?
Let me get all of these in there
This green one
That. Copy and paste it
That. I could keep going, keep drawing velocity vectors around the circle
but let me do this orange one right over here
Copy and paste
So between this magenta time and this purple time
what was the change in velocity?
Well, we could look at that purely from these vectors right here
The change in velocity between those two times was that right over there
That is our change in velocity
So I take this vector and say in what direction was the velocity changing
when this vector was going on this part of the arc
It's roughly--if I just translate that vector right over here
it's roughly going in that direction
So that is the direction of our change in velocity
This triangle is delta; delta is for change
Now think about the next time period
between this blue or purple period and this green period
Our change in velocity would look like that
So while it's traveling along this part of the arc
roughly it's the change in velocity if we draw the vector starting at the object
It would look something like this
I'm just translating this vector right over here
I'll do it one more time
From this green point in time to this orange point in time
and obviously we're just sampling points continuously moving
and the change in velocity actually continues changing
but hopefully you're going to see the pattern here
So between those two points in time, this is our change in velocity
And let me translate that vector right over there
It would look something like that
change in velocity
So what do you see, if I were to keep drawing more of these change in velocity vectors
you would see at this point, the change in velocity would have to be going
generally in that direction
At this point, the change in velocity would have to be going generally in that direction
So what do you see? What's the pattern for any point along this circular curve?
Well, the change in velocity
first of all, is perpendicular to the direction of the velocity itself
And we haven't proved it, but it at least looks like it
Looks like this is perpendicular
And even more interesting, it looks like it's seeking the center
The change in velocity is constantly going in the direction of the center of our circle
And we know from Newton's first law
that if--the magnitude could stay the same but the
velocity change in any way, either the magnitude or the direction or both
there must be a net force acting on the object
And the net force is acting in the direction of the acceleration
which is causing the change in velocity
So the force must be acting in the same direction as this change in velocity
So in order make this object go in this circular
there must be some force kind of pulling the object towards the center
and a force that is perpendicular to its directional motion
And this force is called the centripetal force
Centripetal
Not to be confused with centrifugal force, very different
Centripetal force, centri- you might recognize as center
and then -petal is seeking the center. It is center seeking
So this centripetal force, something is pulling on this object towards the center that
causes it to go into this circular motion
Inward pulling causes inward acceleration
So that's centripetal force
causing centripetal acceleration
which causes the object to go towards the center
The whole point why I did this is that at least it wasn't intuitive to me
that if you have this object going in a circle
that the change in velocity, the acceleration, the force acting on this object
would actually have to be towards the center
The whole reason why I drew these vectors
and then translate them over here and drew these change in velocity vectors
is to show you that the change in velocity is actually towards the center of this circle
Now with that out of the way, you might say, well, where is this happening in in everyday life
or in reality in some way it perform
And the most typical example of this and this is something that I think most of us have done
when we were kid if you had a yoyo
My best attempt to draw a yoyo
If you have a yoyo and if you whip it around on a string
you know that the yoyo goes in a circle
Even though its speed might be constant, or the magnitude of its velocity might be constant
we know that the direction of its velocity is constantly changing
It's going in a circle and what's causing it to go in a circle is your hand right over here
pulling on this string and providing tension into the string
So there's a force, the centripetal force in this yoyo example is the tension in the string
that's constantly pulling on the yoyo towards the center
and that's why that yoyo goes in a circle
Another example that you are probably somewhat familiar with or at least have heard about
is if you have something in orbit around the planet
So let's say this is Earth right here
and you have some type of a satellite that is in orbit around Earth
That satellite has some velocity at any given moment in time
What's keeping it from not flying out into space and keeping it going in a circle
is the force of gravity
So in the example of a satellite or anything in the orbit
even the moon in orbit around the Earth
the thing that's keeping an orbit as opposed to flying out into space
is a centripetal force of Earth's gravity
Now another example, this is probably the most everyday example because we do it all the time
If you imagine a car traveling around the racetrack
Let's draw a racetrack. If I have a racetrack
Before I tell you the answer, I'll have you think about it
It's circular. Let's view the racetrack from above
If I have a car on a racetrack. I want you to pause it before I tell it to you
because I think it's an interesting thing think about
It seems like a very obvious thing that's happening
We've all experienced; we've all taken turns in cars
So we're looking at the top of a car. Tires
When you see a car going at a constant speed
so on the speedometer, it might say, 60 mph, 40 mph, whatever the constant speed
but it's traveling in a circle
so what is keeping--what is the centripetal force in that example?
There's no obvious string being pulled on the car towards the center
There is no some magical gravity pulling it towards the center of the circle
There's obviously gravity pulling you down towards the ground
but nothing pulling it to the side like this
So what's causing this car to go in the circle as opposed to going straight?
And I encourage you to pause it right now before I tell you the answer
Assuming you now unpaused it and I will now tell you the answer
The thing that's keeping it going in the circle is actually the force of friction
It's actually the force between the resist movement to the side between the tires and the road
And a good example of that is if you would remove the friction
if you would make the car driving on oil or on ice
or if you would shave the treads of the tire or something
then the car would not be able to do this
So it's actually the force of friction in this example
I encourage you to think about that