While "centrifugal force" is something we all seem to experience, it truly is a fictitious force. By a fictitious force, I mean that it is a side effect of acceleration and not a cause of acceleration.

There is no true outward force acting on an object that's revolving around a center. Instead, that object's own inertia is trying to make it travel in a straight-line path that would cause it to drift farther and farther away from the center. The one true force acting on the revolving object is an inward one-a centripetal force. The object is trying to go straight and the centripetal force is pulling it inward and bending the object's path into a circle.

To get a feel for the experiences associated with this sort of motion, let's first imagine that you are the revolving object and that you're swinging around in a circle at the end of a rope. In that case, your inertia is trying to send you in a straight-line path and the rope is pulling you inward and deflecting your motion so that you go in a circle. If you are holding the rope with your hands, you'll feel the tension in the rope as the rope pulls on you. (Note that, in accordance with Newton's third law of motion, you pull back on the rope just as hard as it pulls on you.) The rope's force makes you accelerate inward and you feel all the mass in your body resisting this inward acceleration. As the rope's force is conveyed throughout your body via your muscles and bones, you feel your body resisting this inward acceleration. There's no actual outward force on you; it's just your inertia fighting the inward acceleration. You'd feel the same experience if you were being yanked forward by a rope-there would be no real backward force acting on you yet you'd feel your inertia fighting the forward acceleration.

Now let's imagine that you are exerting the inward force on an object and that that object is a heavy bucket of water that's swinging around in a circle. The water's inertia is trying to make it travel in a straight line and you're pulling inward on it to bend its path into a circle. The force you exert on the bucket is quite real and it causes the bucket to accelerate inward, rather than traveling straight ahead. Since you're exerting an inward force on the bucket, the bucket must exert an inward force on you (Newton's third law again). It pulls outward on your arm. But there isn't anything pulling outward on the bucket, no mysterious "centrifugal force." Instead, the bucket accelerates in response to an unbalance force on it: you pull it inward and nothing pulls it outward, so it accelerates inward. In the process, the bucket exerts only one force on its surroundings: an outward force on your arm.

As for the operation of a centrifuge, it works by swinging its contents around in a circle and using their inertias to make them separate. The various items in the centrifuge have different densities and other characteristics that affect their paths as they revolve around the center of the centrifuge. Inertia tends to make each item go straight while the centrifuge makes them bend inward. The forces causing this inward bending have to be conveyed from the centrifuge through its contents and there's a tendency for the denser items in the centrifuge to travel straighter than the less dense items. As a result, the denser items are found near the outside of the circular path while the less dense ones are found near the center of that path.

Whenever you accelerate, you experience a gravity-like sensation in the direction opposite that acceleration. Thus when you accelerate to the left, you feel as though gravity were pulling you not only downward, but also to the right. The rightward "pull" isn't a true force; it's just the result of your own inertia trying to prevent you from accelerating. The amount of that rightward "pull" depends on how quickly you accelerate to the left. If you accelerate to the left at 9.8 meters/second², an acceleration equal in amount to what you would experience if you were falling freely in the earth's gravity, the rightward gravity-like sensation you feel is just as strong as the downward gravity sensation you would feel when you are standing still. You are experiencing a rightward "fictitious force" of 1 g. The g-force you experience whenever you accelerate is equal in amount to your acceleration divided by the acceleration due to gravity (9.8 meters/second²) and points in the direction opposite your acceleration. Often the true downward force of gravity is added to this figure, so that you start with 1 g in the downward direction when you're not accelerating and continue from there. If you are on a roller coaster that is accelerating you upward at 19.6 meters/second², then your total experience is 3 g's in the downward direction (1 g from gravity itself and 2 g's from the upward acceleration). And if you are accelerating downward at 9.8 meters/second², then your total experience is 0 g's (1 g downward for gravity and 1 g upward from the downward acceleration). In this last case, you feel weightless-the weightlessness of a freely falling object such as an astronaut, skydiver, or high jumper.

Note added: A reader pointed out that I never actually answered the question. He's right! So here is the answer: they use accelerometers. An accelerometer is essentially a test mass on a force sensor. When there is no acceleration, the test mass only needs to be supported against the pull of gravity (i.e., the test mass's weight), so the force sensor reports that it is pushing up on the test mass with a force equal to the test mass's weight. But once the accelerometer begins to accelerate, the test mass needs an additional force in order to accelerate with the accelerometer. The force sensor detects this additional force and reports it. If you carry an accelerometer with you on a roller coaster, it will report the force it exerts on the test mass at each moment during the trip. A recording device can thus follow the "g-forces" throughout the ride.

As far as how accelerometers work, modern ones are generally based on tiny mechanical systems known as MEMS (Micro-Electro-Mechanical Systems). Their test masses are associated with microscopic spring systems and the complete accelerometer sensor resides on a single chip.

When an astronaut is orbiting the earth, he isn't really weightless. The earth's gravity is still pulling him toward the center of the earth and his weight is almost as large as it would be on the earth's surface. What makes him feel weightless is the fact that he is in free fall all the time! He is falling just as he would be if he had jumped off a diving board or a cliff. If it weren't for the astronaut's enormous sideways velocity, he would plunge toward the earth faster and faster and soon crash into the earth's surface. But his sideways velocity carries him past the horizon so fast that he keeps missing the earth as he falls. Instead of crashing into the earth, he orbits it.

During his orbit, the astronaut feels weightless because all of his "pieces" are falling together. Those pieces don't need to push on one another to keep their relative positions as they fall, so he feels none of the internal forces that he interprets as weight when he stands on the ground. A falling astronaut can't feel his weight.

To prepare for this weightless feeling, the astronaut needs to fall. Jumping off a diving board or riding a roller coaster will help, but the classic training technique is a ride on the "Vomit Comet"--an airplane that follows a parabolic arc through the air that allows everything inside it to fall freely. The airplane's arc is just that of a freely falling object and everything inside it floats around in free fall, too--including the astronaut trainee. The plane starts the arc heading upward. It slows its rise until it reaches a peak height and then continues arcing downward faster and faster. The whole trip lasts at most 20 seconds, during which everyone inside the plane feels weightless.

A roller coaster is a gravity-powered train. Since it has no engine or other means of propulsion, it relies on energy stored in the force of gravity to make it move. This energy, known as "gravitational potential energy," exists because separating the roller coaster from the earth requires work--they have to be pulled apart to separate them. Since energy is a conserved quantity, meaning that it can't be created or destroyed, energy invested in the roller coaster by pulling it away from the earth doesn't disappear. It becomes stored energy: gravitational potential energy. The higher the roller coaster is above the earth's surface, the more gravitational potential energy it has.

Since the top of the first hill is the highest point on the track, it's also the point at which the roller coaster's gravitational potential energy is greatest. Moreover, as the roller coaster passes over the top of the first hill, its total energy is greatest. Most of that total energy is gravitational potential energy but a small amount is kinetic energy, the energy of motion.

From that point on, the roller coaster does two things with its energy. First, it begins to transform that energy from one form to another--from gravitational potential energy to kinetic energy and from kinetic energy to gravitational potential energy, back and forth. Second, it begins to transfer some of its energy to its environment, mostly in the form of heat and sound. Each time the roller coaster goes downhill, its gravitational potential energy decreases and its kinetic energy increases. Each time the roller coaster goes uphill, its kinetic energy decreases and its gravitational potential energy increases. But each transfer of energy isn't complete because some of the energy is lost to heat and sound. Because of this lost energy, the roller coaster can't return to its original height after coasting down hill. That's why each successive hill must be lower than the previous hill. Eventually the roller coaster has lost so much of its original total energy that the ride must end. With so little total energy left, the roller coaster can't have much gravitational potential energy and must be much lower than the top of the first hill.

It's then time for the riders to get off, new riders to board, and for a motor-driven chain to drag the roller coaster back to the top of the hill to start the process again. The chain does work on the roller coaster, investing energy into it so that it can carry its riders along the track at break-neck speed again. Overall, energy enters the roller coaster by way of the chain and leaves the roller coaster as heat and sound. In the interim, it goes back and forth between gravitational potential energy and kinetic energy as the roller coaster goes up and down the hills.

Let me start with the concept of inertia. Like all objects in this universe, we naturally tend to keep doing what we're doing--if we are stationary, we tend to remain stationary, and if we are moving, we tend to keep moving in a straight line at a steady pace. In fact, the only way that your speed and/or direction of travel (in short, your velocity) can change is if something pushes on you. When that happens, you accelerate (which is to say your velocity changes).

Whenever you accelerate, the various parts of your body can no longer follow their inertia; they must accelerate, too. This acceleration requires forces within your body and you can feel these forces. In fact, they make it feel as though a new type of gravity were acting on the parts of your body. You can't distinguish true gravity from the experience of acceleration because they feel exactly the same. The strength of this gravity-like experience depends on how fast you accelerate and it points in the direction opposite your acceleration. If you accelerate upward, as you do when an elevator first starts moving upward, this gravity-like sensation points downward and you feel extra heavy (the experience of "positive g's") If you accelerate downward, as you do when a rising elevator comes to a stop, this gravity-like sensation points upward and you feel unusually light (the experience of "negative g's") Since there is no fundamental limit to how rapidly one can accelerate, these positive and negative g's can become extremely strong and can easily feel stronger than the true force of gravity. However, when these gravity-like sensations become a few times stronger than gravity itself, they become difficult to tolerate. That's why elevators start and stop gradually and why the turns on roller coasters aren't too sharp.

Gravity provides the energy source for a roller coaster and inertia is what keeps the roller coaster moving when the track is level or uphill. Once the roller coaster is at the top of the first hill and detaches from the lifting chain, the only energy it has is gravitational potential energy (and a little kinetic energy--the energy of motion). But once it begins to roll down the hill, its gravitational potential energy diminishes and its kinetic energy increases. Since kinetic energy is related to speed, they both increase together.

At the bottom of the first hill, the roller coaster has very little gravitational potential energy left, but it does have lots of kinetic energy. The roller coaster also keeps moving, despite the absence of gravitational potential energy. You can view its continued forward motion as either the result of having lots of kinetic energy or a consequence of having inertia. Inertia is a feature of everything in our universe--a tendency of all objects to keep doing what they're doing. If an object is stationary, it tends to remain station. If an object was moving forward at a certain speed, it tends to keep moving forward at a certain speed. Inertia tends to keep the roller coaster moving forward along the track at a certain speed, even when nothing is pushing on the roller coaster. While the roller coaster will slow down as it rises up the next hill, its inertia keeps it moving forward.

Your true weight is caused by gravity--it is the force exerted on you by gravity; usually the earth's gravity. Your apparent weight is the sum of your true weight and a fictitious force associated with your acceleration. Whenever you accelerate, you experience what feels like a gravitational force in the direction opposite your acceleration. Thus when you accelerate to the left, you feel a gravity-like experience toward your right. It is this effect that seems to throw you to the right whenever the car you are riding in turns toward the left. In fact, this effect is caused by your own inertia--your own tendency to travel in a straight line at a constant speed. Your apparent weight can be quite different from your true weight. Perhaps the most striking example occurs on the loop-the-loop of a roller coaster. While your true weight remain downward throughout the ride, as it always is, your apparent weight actually becomes upward as you pass around the top of the loop-the-loop. You are accelerating downward so rapidly at the top of the loop that the experience you have is one of a gravity-like force that is pulling you skyward. Since the car you are riding in is invert and above you, you feel pressed into your seat even though the ground is in the other direction.

A roller coaster is essentially a gravity-powered train. When the chain pulls the train up the first hill, it transfers an enormous amount of energy to that train. This energy initially takes the form of gravitational potential energy--energy stored in the gravitational force between the train and the earth. But once the train begins to descend the first hill, that gravitational potential energy becomes kinetic energy--the energy of motion. The roller coaster reaches maximum speed at the bottom of the first hill, when all of its gravitational potential energy has been converted to kinetic energy. It then rushes up the second hill, slowing down and converting some of its kinetic energy back into gravitational potential energy. This conversion of energy back and forth between the two forms continues, but energy is gradually lost to friction and air resistance so that the ride becomes less and less intense until finally it comes to a stop.

While roller coasters could be made faster if they used the high performance tracks of bullet trains, smoothing out the tracks would only make the ride less jittery and wouldn't reduce the accelerations needed to complete the turns. The faster the train moves, the faster everything must accelerate as the track bends. Doubling the speed of the roller coaster would double the changes in velocity associated with each bend and would halve the time available to complete that change in velocity. As a result, doubling the roller coaster's speed would quadruple the accelerations it experiences on the same track and thus will quadruple the forces involved during the ride. A roller coaster ride already involves some pretty intense forces and accelerations. If those forces and accelerations were increased by a factor of 4, they would be more than most people could handle. Thus I wouldn't expect many riders on a double-speed bullet train roller coaster.

Building an environment that made you feel what appeared to be the earth's gravity would be a substantial undertaking. The only way to simulate gravity is through acceleration and the only way to make a person experience acceleration continuously is to swing them around in a circle. So this environment will have to swing its occupants around in a circle. However, we are extremely sensitive to changes in orientation, so that we can tell the difference between true gravity and the experience of being swung around in a small circle. To avoid the dizzying feeling of having our orientations changed rapidly, the turning environment would have to be extremely large. It would have to be a huge rotating wheel, looking like a heavily banked circular racetrack that spun at a steady pace and completed something like one full turn per minute. The occupants would have to live on the long, thin surface of this turning racetrack. Building such a device on earth wouldn't be easy. Building it on the moon would be much harder. I wouldn't plan on trying to simulate the earth's gravity on the moon. So I vote for just putting up with the moon's weaker gravity.

Whenever you accelerate, you feel a gravity-like sensation "pulling" you in the direction opposite your acceleration. What you feel isn't really a force--it's really just your own inertia trying to keep you going in a straight line at a constant speed. In other words, your inertia is trying to keep you from accelerating. For example, whenever you turn left in a roller coaster, your inertia opposes your leftward acceleration and you feel "pulled" toward the right. This "pull" of inertia is sometimes called a "fictitious force" but you should remember that it isn't a force at all, no matter how "real" it feels. Perhaps the most striking effect of acceleration occurs during your trip around a vertical loop-the-loop. When you are arcing around the top of the loop-the-loop, you are accelerating downward so quickly that you feel an enormous "fictitious force" upward. This "fictitious force" has a stronger effect on you than the real force of gravity, so you feel as though you are being pulled upward. The result is that you feel pressed into your seat, even though your seat is actually upside-down.

In the lecture, I said that a person who is falling does not feel the effects of gravity, even when they are traveling upward. But when they are falling, they are accelerating downward at a very specific rate--the acceleration due to gravity, which is 9.8 meters/second2 at the earth's surface. When an astronaut is accelerating upward during a launch, they are not falling and they do feel weight. In fact, because they are accelerating upward, they feel particularly heavy.

In principle, yes, but in practice, no. To explain why, I'll begin with the origins of directional circulations on earth. Because the earth is turning, motions along its surface are complicated. The ground at the equator is actually heading eastward at more than 1000 miles per hour. The ground north or south of the equator is also heading eastward, but not as quickly. The ground's eastward speed gradually diminishes until, at the north and south poles, there is no eastward motion at all. As a result of this non-uniform eastward motion of the ground, objects that travel in straight lines because of their inertia end up drifting eastward or westward relative to the ground. For example, if you took an object at the equator and threw it directly northward, it would drift eastward relative to the more slowly moving ground. If someone else threw an object southward from the north pole, that object would drift westward relative to the more rapidly moving ground. In the northern hemisphere, objects approaching a center tend to deflect away from that center to form a counter-clockwise circle around it. This process is reversed in the southern hemisphere so that objects approaching a center there tend to form a clockwise circle around it. Thus hurricanes are counter-clockwise in the northern hemisphere and clockwise in the southern hemisphere.

When water drains from a basin in the northern hemisphere, it flows toward a center and should have a tendency to deflect into a counter-clockwise swirl. However, the effect is very weak in a small washbasin. The direction in which the water swirls as it drains is determined by other effects such as how the water was sloshing before you opened the drain or how symmetric the basin is. For this earth's rotation-driven swirling effect (the Coriolis effect) to dictate the direction of a circulation the objects involved must move long distances over the earth's surface. Even tornadoes don't always rotate in the expected direction; they're just not big enough to be spun consistently by the Coriolis effect.

There are many indirect indications that the earth rotates, including the motions of celestial objects overhead, the earth's winds--particularly the counter-clockwise rotation of surface winds in northern hemisphere hurricanes, and the outward bulge of the earth around its equator. But for a more direct indication, a Foucault pendulum is a good choice.

Unfortunately, a Foucault pendulum isn't easy to interpret or build. It would be easiest to interpret if it were at the north pole, where it would swing back and forth in a fixed plane as the earth turned beneath it. To a person watching the pendulum from the ground, the pendulum's swinging arc would appear to complete one full turn each day. However, elsewhere in the northern hemisphere, the plane of the pendulum does change and the pendulum's swinging arc will appear to complete less than one full turn each day. Nonetheless, the fact that the arc shifts at all is an indication that the ground is accelerating and that the earth is turning.

The problem with building a Foucault pendulum is that it must retain its swinging energy for hours or even days and that it must not be perturbed by activities around it. It must have a very dense, massive pendulum bob supported on a strong, thin cable and that cable must be attached to a rigid support overhead. The longer the cable is, the longer it will take the bob to complete each swing and the more slowly the pendulum will move. Slow movements are important to minimize air resistance. If I were building a Foucault pendulum, I'd find a tall empty shaft somewhere, away from any moving air, and I'd attached a lead-filled metal ball (weighing at least 100 pounds but probably more) to the top of the shaft with a thin steel cable. I'd make sure that nothing rubbed and that the top of the cable never moved. (Over the long haul, there is the issue of damage to the top of the cable because of flexure...it will eventually break here. Wrapping the cable around a drum so that there is no specific bending point helps.) Then I'd pull the pendulum away from its equilibrium position and let it start swinging slowly back and forth. Over the course of several hours, its swing would decrease, but not before we would notice that its arc had turned significantly away from the original arc because of the earth's rotation.

I'll assume that the car starts on a slope and coasts downhill to a level finish. If that's the case, then you want to put the car's center of gravity as far back in the car as you can get it. That way, the center of gravity will start as high as possible in the tilted car and will finish as low as possible in the level car. During a race, the car obtains its kinetic energy (its energy of motion) from its gravitational potential energy. The farther the car's center of gravity descends during the race, the more gravitational potential energy will be converted to kinetic energy and the faster the car will go.

The car's biggest obstacle is air resistance, which in this case is a force known as "pressure drag." The pressure drag force is proportional to the size of the turbulent wake the car creates in the air as it passes through the air. Streamlining is important to minimizing this wake. The thinner and shorter you can make the car, the smaller its wake will be. The ideal shape would be an airfoil, like those used in airplane wings and bodies. These carefully tapered shapes barely disturb the air at all and experience very little pressure drag. If you design your car to resemble a wingless commercial jet airliner, you will be doing pretty well.

A real force causes acceleration. If the outward "fictitious" force on a circling object were "real," that object wouldn't circle. It would accelerate outward. When you swing an object around on a string, you feel the object pulling outward on the string. But it isn't itself being pulled outward by anything. What you're feeling is the object's inertia trying to make it travel straight. The inward force you're exerting on it isn't opposing some real force, it's causing the object to accelerate inward.

Yes. As you whip the object around on a string, you are doing work on it. You do this by making subtle movements with your hand, exerting forces that aren't exactly toward the center of the circle. When you do this, the object begins to travel faster and faster, so its kinetic energy increases. Traveling in a circle doesn't change this kinetic energy because kinetic energy is proportional to speed squared, and doesn't depend on direction. Finally, when you let go of the string, the object stops circling and begins to travel in a straight line. It carries with it all the kinetic energy you gave it by whipping it about.

Let's neglect gravity, which isn't important in this horizontal motion problem. When a ball swings in a circle at the end of a string, there is only one force on it and that force is inward (toward the center of the circle). We call such a force a centripetal force, meaning toward the center. There are many kinds of centripetal forces and the string's force is one of them. As for the ball's tendency to travel in a straight line, that's just the ball's inertia. With no forces acting on it, it will obey Newton's first law and travel in a straight line. There is no real force pulling the ball outward. But a person riding on the ball will feel pulled outward. We call this feeling a fictitious force. Fictitious forces always appear in the direction opposite an acceleration. In this case (an object traveling in a circle) the outward fictitious force is called centrifugal "force." But remember that it's not a real force; it's just the object's inertia trying to make it go in a straight line.

As you travel over the top of the loop the loop, you observe the world from an inverted perspective. The sky is below you and the ground is above you. If you were to take a coin out of your pocket and release it, you would see it fall toward your seat. From that observation, and the feeling of being pressed into your seat, you might think that gravity is suddenly pulling you toward the sky. It isn't. Gravity is still pulling you toward the ground, but you are in a car that is accelerating rapidly toward the ground. As a result, the car is having to push you toward the ground with a force on the seat of your pants. You feel pressed into your seat because the car is pushing you downward hard. When you release the coin, it seems to fall toward the sky, but it's really just falling more slowly than you are. With the car pushing you downward, you're accelerating toward the ground faster than the coin and you overtake it on the way down. It drifts toward the seat of the car because the car seat accelerates toward it. As you can see, the only forces around are the force of gravity and support forces from the car. There is no outward or upward force here. The fictitious force is truly fictional; a way of talking about the strange pull you feel toward the outside of the loop.

Yes. If you go over a loop-the-loop too slowly, so that you don't accelerate downward quickly enough, you will leave the track and fall. That's why some roller coasters strap you in carefully before taking you upside-down slowly. Without the supports, you would fall out of the car.

Yes. When the kids move away from the center, the merry-go-round will slow down. If they then return to the center, the merry-go-round will speed up!

Centripetal means "directed toward a center." A centripetal force is a force that's directed toward a center. For example, a ball swinging around in a circle at the end of a string is experiencing a force toward the center of the circle--a centripetal force. Because the ball accelerates in the direction of the force, it accelerates centripetally. And because it experiences a fictitious force in the direction opposite its acceleration, it experiences an outward fictitious force away from the center of the circle. That fictitious force is called centrifugal "force." However, you should always recognize that this outward "force" is not a force at all, but an effect caused by the ball's inertia--its tendency to travel in a straight line.