Main content

## AP®︎/College Physics 1

### Course: AP®︎/College Physics 1 > Unit 3

Lesson 6: Free-body diagrams for objects in uniform circular motion# Identifying centripetal force for cars and satellites

AP.PHYS:

INT‑3.B (EU)

, INT‑3.B.2 (EK)

, INT‑3.B.2.1 (LO)

Identifying forces or force components acting as the centripetal force for a car driving in a horizontal circle, a car driving in a vertical circle, and a satellite in orbit.

## Want to join the conversation?

- At2:19, shouldn't the frictional force point in the opposite direction of the velocity?(33 votes)
- The frictional force is opposite to whatever force that is causing motion. In this case, it is the force of moving [a point] on the wheel of the car. To rotate the wheels, the wheels need to exert a force on the road, and to resist this motion (Newton's 3rd Law), the road pushes back on the wheel in the opposite direction. Therefore the car moves.(22 votes)

- At8:07, if the only force in the y-direction is downwards then why doesn't the car fall down?(16 votes)
- The car does accelerate downward at the moment, however after this acceleration downward, at the very next moment, the normal force is at a different angle, perpendicular to the surface. Due to this, the car continues in a circular motion. If the very top of the circle is the end of the car's path, then it will fall down.(12 votes)

- Why is there friction going forwards? I don't understand that part in the free body diagram? Isn't friction usually opposite of the motion?(13 votes)
- how can air friction be counteracted by frictional force ,and why is friction on the direction of motion?(5 votes)
- When a human is walking she is pushing on the ground or, more precisely, she is pushing the ground backward. Actually, you could go as far as to say that she is pushing the ground backward while trying to make her foot slide back... but the friction force prevents this from happening!

That's why friction force is exerted on the opposite direction making her body accelerate forward.

The situation is a bit more complicated when talking about wheels but the principle is the same.

About the second question, it is safe to assume that air friction slows you down no matter where you are going (the soundest argument for me is to say that you convert a fraction of your kinetic energy to heat).

So, if you want to keep moving through air, you need at the very least to counteract its tendency to slow you down. If i did a good job convincing you that friction is in the direction of motion (obvious exceptions apply, i can explain this further if you want me to) then it's now clear that frictional force actually counteracts air friction.(8 votes)

- At4:50, where does the extra Fn comes from?(6 votes)
- The normal force Fn is provided by the
**loop's surface**itself. If you're wondering why/how is it larger than Fg, I guess it's because the*'loop-y '*surface is pushing the car towards the center of the circle at every point more than gravity is pulling it downwards.(2 votes)

- If the direction of the force of friction is always opposite to the direction of motion, why does it point inwards to the center of the circle?

The car is clearly not moving opposite to this force, isn't it?2:50(3 votes)- the cars tyres use the frictional force to go forward, and if you turn the wheels left the frictional forces with the road will push you left- or if you turn the wheel towards the centre of the circular path the frictional forces will be the net force/centripetal force.(4 votes)

- Are we assuming that the cars' engines are turned off? So they are not exerting any driving force?(4 votes)
- We don't count the car's engine as a force being applied.(0 votes)

- At the top of the loop de loop, Both the normal force and the gravitational force are acting towards the center of the loop. So what prevents the car from falling downwards? Thank You.(2 votes)
- Gravity is taking the place of the centripetal force. In this case, we need something to counter gravity.

Think of the car, and recall Newton's First Law. The Car wants to move constantly in a straight line. But the shape of the loop de loop keeps it in its path. As it wants to keep moving in a straight line, this accounts for the ficticious centrifugal force. For the driver in the car, it seems like centrifugal force. But for us outside, we see that its just Newton's First Law pushing the car against the railing and canceling the forces of gravity.

So what prevents the car from falling downwards?

Its just centrifugal force (or Newton's First Law depending on what perspective you are looking a

If you are wondering how gravity is a centripetal force:

There is no force called "centripetal force" on its own, its just a recreation of other physical everday forces we experience in our everyday lives.

If you take a tennis ball and tie it to a string and whip it around your head, the tension forces act as the centripetal force, its not centripetal force on its own.

For a race car speeding down a curve, friction acts like the centripetal force, keeping it on its path.

For the particle, the magnetic field's force that acts like the centripetal force when it moves in a circular motion.

Likewise, same for other forces, gravity must be acting like the centripetal force in this case.(3 votes)

- Why is the normal force greater than the force of gravity at4:50.(2 votes)
- In order to keep the car moving upwards, the normal force has to be greater than gravity, which wants to keep the car on level ground. The inward, normal force has to be greater than the force of gravity when entering the loop.(3 votes)

- In our science class, it was explained to us that the moon orbits the Earth because of gravity and inertia. Why didn't Sal mention inertia?(2 votes)
- Inertia isn't a force; in fact, it's not even a quantity. This video focuses on identifying forces. Hope that I helped.(3 votes)

## Video transcript

- So here we have something
that you probably have done in the last, maybe in the last day. And if we're in a car and
we're just making a turn, let's say at a constant
speed, on a road that is flat. So it's not a banked race
track or anything like that. What is keeping the car from just veering off in a straight line? And this one's a little bit less intuitive because we don't have any string here that's tethering the car to the center of the curve of our road. So what's keeping it from
going in a straight line here? Pause the video and think about that. Well in this situation,
and we could think about other forces that are at play. And once again I'll
assume we're in a vacuum, although you could think
about air resistance as well and think about what is
counteracting the air resistance. It turns out that that's friction. But the other forces at play, you of course have the force of gravity pulling downward on the
car, force of gravity. And that's being counteracted
by the normal force, that's being counteracted
by the normal force. Force, the normal force
of the road on the car. But what's keeping the
car going in a circle? And actually let's just
do air resistance for fun. So the air resistance, the
force of the air on the car, that's gonna be pushing
in the direction opposite from the velocity of the car. So we could call that, let's
just call that force of air. You can't read that, let me do it this. So, force of the air, that
would be its magnitude. And then that's being counteracted by, and this is a little bit counterintuitive, and this will actually give us a clue on the centripital force,
that is this component, that is being counteracted
by this component of the friction, so force of friction, in the direction that the car is going. Think about it, if you didn't have-- if this was ice on ice, if the
wheels didn't have traction, no matter how hard the engine went and no matter how fast the wheels sped, it wouldn't be able to
overcome the air resistance, and then the car would decelerate. But these are all the
forces that aren't acting in a radial direction,
that aren't keeping the car on the road, so to speak,
or keeping it going in that circular motion around the curve. The one there, is once
again, the force of friction. So this is another, I guess you could say, another component of
the force of friction. And that's happening where the tires, where the literally, the
rubber meets the road. But this right over here, you
have the force of friction, that is keeping, and maybe I'll call it force of friction radially, radially. We'll put it in parentheses. Force of friction, radially. That is keeping us going
in a circular direction. And so, in this situation,
that is our centripetal force. Let's do another example,
and let's keep going with the theme of cars now. So let's say a scenario where, we are on a loop-de-loop, which is always fun, and kind of scary. I have dreams where I have
to drive on loop-de-loop, for some reason, and I
find it intimidating. But let's think about the
car at different points of the loop-de-loop, and
think about what is-- what is the centripetal
force at different points. So let's first think about
this point right over here. And, once again, we assume
that we are dealing, we're on a planet, and so you
have your force of gravity, right over here, force of gravity. And then, you also have your normal force. And I'm going to draw
it a little bit larger, because in order to be
moved, I guess you could say, upwards, to stay on the loop-de-loop, the normal force has to be larger, you have to have a net force inward. So this is "F," this is our normal force. And so, in this situation, the magnitude, the magnitude of our centripetal force, let me do this in a different color. The magnitude of our
centripetal force is going to be the net radial inward radial force, for the magnitude of the
net radial inward force. So this would be equal to the
magnitude of our normal force minus, minus the magnitude
of the force of gravity. If this wasn't net inward right over here, then you would not, this car would not be able to move in a circle. It would just, if this netted out to zero, it would go in a straight line that way. And if this netted out
so that it was negative it would accelerate downwards. So, let's go at this
point right over here. And we could also think about
things like air-resistance and friction, where
air-resistance is pushing back on the car, and friction is overcoming it, but we're going to focus
just on the things that are driving us centripetally
inward or outward right now. Now what about this point for the car? Well, we still have the force of gravity, you still have the force of gravity. And actually, I'll make
this a little bit bigger. We could-- eh, let me put
the air-resistance there, just to be complete. So this would be the air
resistance, force of the air, and then that's being
counteracted by force of friction, the traction that the
car has with the road. Over here, this orange
vector, this would now be the combination of the force of gravity. And actually, you could even consider it the force of gravity,
plus the, plus the force, the air resistance, plus
the force of the air pushing back on the car,
the pressure of the air. And then that is being counteracted by the force of friction,
so the force of friction of the tires of the
tires pushing, pushing-- Or I guess, the force
of friction of the tire, between the tire and the road. But neither of these are
acting centripetally, acting radially inward. So, what's that going to be? Well, here you have the
normal force of the track. The track is what's keeping this car going in this circular direction. And so you have, so you have-- Here, the inward force is
the normal force, F normal. So in this situation,
our centripetal force, the magnitude of our
centripetal force is equal to the magnitude of our normal force. And these, actually, are
even going to be the same, the exact same vectors. Now, let's consider one last scenario. When we are at the top
of the loop-de-loop. Pause the video, and see
if you can figure that out. Well, once again, we can do things like, we could say, hey look, there's
probably some air-resistance that is keeping us, that
is trying to decelerate us. So that, and then that's being, that's being netted out
by the force of friction. But let's think about what's going on in the vertical direction. So here, pushing down this way, you're going to have,
potentially several forces, and I want this to actually
be at the top of the loop-de-loop, although it
doesn't look quite like that, but actually let's just assume it is. We're at the top of the loop-de-loop. Pushing down, you're going
to have the force of gravity. But what else are you going to have? Assuming you're going fast enough, the track is also pushing down. The force of gravity
plus the normal force. The magnitude of this vector
would be the magnitude, it would be the sum of the magnitudes of the gravitational force
and the normal force. And that is what's providing
your centripetal force there. And so, in this scenario, we would say the magnitude of our centripetal force is equal to the magnitude
of our gravitational force plus the magnitude of our normal force. Or, we could even think
about it as vectors. We could say, hey look, if
we just add up these vectors, these two vectors, you're going to get your centripetal force vector. That's what keeps the car
going in that circular motion. Now let's just do one last
scenario, just for fun. Let's imagine that we
have an object in orbit. So, this is our planet,
or any planet really. And you have an object in
orbit, some type of a satellite. I'll draw what we normally
associate with as a satellite. But this could be even
a natural satellite, a moon for the planet,
and what I'm about to say applies to the moon as well. So here, we don't have air, we have very minimal air resistance, there might be a few molecules
every here and there. But for the most part,
this is in a vacuum, and it's in orbit, so what keeps-- So it's in a uniform circular motion, it's moving in a circular
orbit around the planet. What keeps it going
off in a straight line? Pause the video and think about it. Well here, you have the force of gravity. You have the force of
gravity of the planet. So right there, you have
the force of gravity. And at first people
say, wait wait, gravity? I see these picture of astronauts floating when they're in orbit. Well, that's just because
they're in free-fall. But the gravity at that point,
if you're a few hundred miles above the surface of the
Earth, is not that different than the gravity on the
surface of the Earth. You just don't have air there,
and if you are in orbit, you're in constant free-fall, so it feels, to you,
like there is no gravity. But it's gravity that is
keeping you on the orbital path, on that circular path, and
keeps you from just going in a straight line out into space.