Main content

## Physics library

### Unit 4: Lesson 1

Circular motion and centripetal acceleration- Race cars with constant speed around curve
- Centripetal force and acceleration intuition
- Visual understanding of centripetal acceleration formula
- What is centripetal acceleration?
- Optimal turns at Indianapolis Motor Speedway with JR Hildebrand
- Calculus proof of centripetal acceleration formula
- Loop de loop question
- Loop de loop answer part 1
- Loop de loop answer part 2

© 2022 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Race cars with constant speed around curve

When acceleration could involve a change in direction and not speed. Created by Sal Khan.

## Video transcript

So we have some race
cars racing, right here. And I have an interesting
question to ask you. If we assume that these
cars are making this turn right over here,
that all of them are making this turn at
a constant speed of 100 kilometers per hour, my
interesting question for you is, are these cars accelerating
while they make this turn? So is acceleration happening? And you might say, well, gee,
look, my speed was constant, it's not changing. If I looked at the
speedometer for the car here, if I looked at the
speedometer over here, it won't budge, it just stays
at 100 kilometers per hour. I don't have any change
in speed over time. And so then you
might say that you don't have any acceleration. But then you might
be saying, well, why would Sal even
make this video? And why would that question
even be interesting? And your second
suspicion would be true, because these cars
actually are accelerating despite having a constant speed. And you can pause it and
think about that for a second, if want to. But I wanted to point
this out to you, because in an example like this,
the difference between speed and velocity starts
to matter, speed being a scalar quantity
only having a magnitude. And velocity being
a vector quantity, being speed with a
direction, having a magnitude and a direction. And to think about-- let's
take a top view of this thing, and then I think it'll
become a little bit clearer the difference between
speed and velocity and why these things
are accelerating. So if I were to take a top
view of this racetrack-- I'll do my best
attempt to draw it-- so it might look
something like this. This is the top view. I could even draw
this red and white. So red, just to
give you the idea. So this is the red, and
there's some white in between. Obviously I'm not
drawing as many dividers as there are in
the actual picture, but it gives you an idea of
what I'm actually drawing. And then there's
some grass out here, there's some grass
over here, and then there's some grass over here. And let's focus on this orange
car and this red car right over here. And this is a top view, so this
is its path right over here. And we're saying it
has a constant speed of 100 kilometers per hour. So if you think
about its velocity, the magnitude of it's
velocity is constant, it's 100 kilometers per hour. But what is happening to the
direction of the velocity? Remember, velocity
is a vector quantity. It has magnitude and direction. So up here, when it's
starting to enter the curve, it's going in this direction. And you tend to show
vectors by arrows like this. And what you do is,
the arrow's going in the direction of the
velocity, in this case, and normally you would draw
the length of the arrow shows what is the velocity. The magnitude of the
velocity, I should say. So it's velocity's constant. So the length of this arrow
will always be constant. But as we see, it's
direction changes. When it's halfway
through the turn, it's not going in
that same direction. It is now going in a
different direction, and when it comes to
the bottom of the turn, it's going in a very
different direction. And the direction keeps changing
as long as it is turning. And I'm not going to
go into the math here. We're going to wait for the
math on this a little bit later. But remember, acceleration is
a change in velocity over time. Acceleration is equal to a
change in velocity over time, or we could say over
a change in time. And although the velocity's
magnitude is constant here, it's direction is changing. If there was no
acceleration on it, it's magnitude and the
direction of it's velocity would be constant,
and the car would just keep going in that direction. So somehow, the
car's direction is changing inward over
and over and over again. And so this is just kind
of a little bit of a trick question, something
for you to think about, we're going to discuss
the math in more detail in future videos. But what's happening here is the
cars actually are accelerating. And they're actually
accelerating inwards, and that's what's
changing inwards. And when I say inwards,
they're being accelerated towards the center of
the curve, and that's what's allowing their
direction to actually change.