Introduction to centripetal force | AP Physics 1 | Khan Academy

- [Instructor] Just for kicks,

let's imagine someone
spinning a flaming tennis ball

attached to some type of a string or chain

that they're spinning it
above their head like this

and let's say they're spinning
it at a constant speed.

We've already described
situations like this,

maybe not with as much drama as this one

but we can visualize the velocity vectors

at different points for the ball.

So, at this point, let's
say the velocity vector

will look like this,

the linear velocity vector
just to be super clear.

So, the linear velocity vector

might look something like that

and it's going to have magnitude V,

the magnitude of the velocity vector

you could also view as its linear speed.

Now, a few moments later,

what is the ball going to be doing?

Well, a few moments later

the ball might be let's
say right over here,

we don't wanna lose the drama,

it's still flaming we're assuming,

it's still attached to
our chain right over here

but what would its velocity vector be?

Well, we're assuming it
has a constant speed,

a constant linear speed,

so the magnitude is going to be the same

but now the direction is
going to be tangential

to the circular path at that point.

So, our direction has changed.

Now, one way to think about this change

in direction of velocity,

it's a little counterintuitive at first

because when we first
think about acceleration,

we tend to think in terms
of changing the magnitude

of velocity but keeping
the magnitude the same,

but changing the direction

still involves an acceleration

and at first, it's a
little counterintuitive

the direction of that acceleration

but if I were to take this
second velocity vector

and if I were to shift it over here,

and if I were to start it
at the exact same point,

it would look something like this,

actually, let me do it in
a slightly different color

so it's a little bit more visible,

so it would look something like this.

This and this, they have the same length

and they're parallel, so
they are the same vector

and so, in some amount of time,

if you wanna go from this velocity vector

and actually this should
be a little bit longer,

this should look like this,

it should have the same
magnitude as this one,

so it should look like this.

So, if in some amount of time,

this and this should
have the same magnitude.

If in some amount of time

you go from this velocity vector

to this velocity vector,

your net change in velocity

is going radially inward.

This right over here is
your net change in velocity

and so, in other videos

we talk about this notion
of centripetal acceleration.

In order to keep something going

in this uniform circular motion,

in order to keep changing the direction

of our velocity vector,

you are accelerating it radially inward,

centripetal acceleration,
inward acceleration

and so, at all points in time,

you have an inward acceleration

which we denote, the magnitude,

we usually say is A with a
C subscript for centripetal.

Sometimes you'll see an A
with an R subscript for radial

but in this context we
will use centripetal.

Now, one question that you
might have been wondering

this whole time that we talked

about centripetal acceleration

is Newton's First Law might be nagging.

Newton's First Law tells
us that the velocity

of an object both it's
magnitude and its direction

will not change unless
there's some net force

acting on the object

and we clearly see here

that the direction of our
velocity vector is changing,

so Newton's First Law tells us

that there must be some
net force acting on it

and that net force is going to be acting

in the same direction as our acceleration

and so, what we're gonna do here

is introduce an idea of centripetal force.

So, centripetal force,

if it's accelerating the object inwards

in the inward direction,

so we have a centripetal force

that is causing our
centripetal acceleration.

F sub C right over here,

you can view that as the
magnitude of our centripetal force

and the way that they would be connected

comes straight out for
Newton's Second Law.

This isn't some type of new,
different type of force,

this is the same type of forces

that we talk about throughout physics.

We know that the magnitude
of our centripetal force

is going to be equal to
the mass of our object

times the magnitude of our
centripetal acceleration.

If you want, you could put
vectors on top of this.

You could say something like this

but we know the direction
of the centripetal force

and the centripetal
acceleration, it is inward.

Now, what inward means,

the exact arrow's going to be different

at different points but for
any position for the ball

we know at least conceptually

what inward is going to be.

So, this is just to appreciate the idea.

Centripetal acceleration
in classical mechanics

isn't just going to
show up out of nowhere.

Newton's First Law tells us

that if something is being accelerated,

there must be a net force acting on it

and if it's being accelerated inward

in the centripetal direction
I guess you could say,

then the force must also be acting inward

and they would just be
related by F equals MA

which we learn from Newton's Second Law.

And to appreciate the intuition for this,

just remember the last time

that you were spinning or
rotating a flaming tennis ball

attached to a chain above your head.

In order to do that, in order
to keep the ball spinning

and not just going and veering
off in a straight line,

you can keep pulling inward on your chain

so that the flaming tennis
ball doesn't go hit a wall

and set things onto fire.

And so, what you are providing
is that centripetal force

to keep that flaming tennis ball

in its uniform circular motion.