I’ve had my first controversy at the Bee. And no, I didn’t bobble a sensitive issue like immigration law or global warming or politics or even genetic engineering like you’d expect. The controversy is over centrifugal force. Weirdly enough, everybody’s talking about physics.
As far as controversies go, it could be a lot worse. I could have been nominated for Michelle Malkin’s Jerk of the Year like Bobby who sits a couple desks from me at the Bee. Or worse, with everybody on the editing staff shooting nervous looks my way, I could have been wrong.
But I’m not : )
In journalism, I’ve noticed, pedigree is a must. The “experts” we cite in our stories, for instance, have doctorates from this-and-that university but we know little about them beyond that. Yet, with the alphabet soup after their names, we trust them any how (and for good reason). Science writers, though, don’t get that luxury. We just get a by-line.
When I got my first email that I should go learn some physics before I tried to write about it, I laughed. It hadn’t occurred to me that I’d written anything controversial. Then a second email came to elaborate. Apparently I had mistakenly attributed to friction something that was obviously the work of centrifugal force. The buzz was over a line I’d tossed into the end of the story, in a section thinned out by editorial needs. I had said this:
Not too far away, a bowl-shaped ride called Starship 3000 spins up and riders find themselves glued to the wall. When the wall rises, feet leave the ground. It’s not magic – just friction.
The story came out front page yesterday, with sweet photos too, might I add:
Scott had thought it would be fun to look into the science of fair rides. So I did. I made a list of the most physically interesting rides at the fair. But the best stuff came from a conversation with a NIST scientist who had studied the Tilt-a-Whirl. Last month I went with John and his sister Andrea to the San Mateo County Fair. I held their stuff while they went whirling around on there. The motion of the cars on the ride reminded me of the double pendulum that hung in the first floor of UC Santa Cruz’s physics building. The one with the sign on it about unpredictable motion… warning you not to get too close. I said so at the time but then forgot about it. When Scott came to me with this fair idea, I showed him a video of a double pendulum on Youtube and started looking into chaos theory papers.
Paring chaotic motion down to a couple of paragraphs was challenging. I was a little afraid I went the sensationalist route with what is most interesting over what is most important. But no matter, all anybody cared about was the sentence describing why you don’t fall down on the Gravitron ride when the floors drop or the walls lift. It’s not magic – just friction.
Here’s why I’m right.
Consider two reference frames. One inside the gravitron (A), spinning with the gravitron, and one outside (B) , stationary with respect to the trees and the tents and a motionless observer. Seen from reference frame B, reference frame A is spinning. Seen from reference frame A, reference frame B is spinning. So you think maybe you can’t tell the difference between the two frames. But you can. Even if your eyes don’t tell you you’re spinning (inside the gravitron), you still get dizzy, right? In one frame, if you put a ball on the ground and let go of it, it doesn’t move (B). In the other, it suddenly starts to roll of its own accord toward the walls (A). The first is the inertial frame. [In a way… the presence of gravity makes it not a true inertial frame but we can ignore that for now]
In an inertial frame objects at rest do NOT begin to move unless there is a force exerted on them. Moving objects do not spontaneously change direction or speed. The inertial frame is where we’ve formulated our laws of Newtonian Mechanics. Let’s see for a second what observer B says happens to observer A’s ball (top of Figure 1).
We notice, as observer B, that observer A is not standing still at all. He’s moving quite rapidly in a circle. When he lets go of the ball, the ball is traveling with horizontal velocity towards us. It travels in a straight line until it runs into the spinning wall eventually. In our frame of reference, this is very natural. A ball that was let go with an initial velocity continued to travel in that direction with the same velocity until it ran into an obstacle.
What does observer A see?
Observer A thinks he is at rest. He lets go of a ball at rest. It accelerates towards the (stationary) walls suddenly, curving a bit on its path, and eventually hits the wall. That’s pretty weird, he thinks. There must be some force causing it to be pulled outward. He deduces two forces which are intrinsic to the motion of any object in his frame. The centrifugal force and the coriolis force, he calls them.
Observer B immediately sees his folly. Observer A is trying to map motion in a non-inertial frame. To observer B, the ball simply traveled in a straight line. It’s the Gravitron which has rotated and collided with the ball.
So what is this centrifugal force everybody keeps talking about? It’s essentially a mathematical short cut. A fictitious force that allows us to consistently formulate physics in a rotating frame of reference.
But it has to be real because we feel it right? If we lean against the walls of a very quickly rotating Gravitron we feel a force holding us against the wall, almost a gravity that is directed outward.
Actually, what you’re feeling is a series of continuous collisions with the same spot on the wall. Like the ball in our earlier scenario. Your inertia wants to take you in a straight line, the walls don’t allow that. The walls exert a force on your body to keep it in circular motion. This force is termed the normal force, since it acts perpendicular to the wall. The component of the normal force pointing toward the center of motion is called the centripetal force. This is the force that is equal to mv^2/R if you are moving in a circle, pointing inward. Centripetal forces could be gravity itself (in the case of an astronaut orbiting the moon), string tension (in the case of a weight swinging around on a string), or friction (in case of someone standing on a merry-go-round), or in this case, the normal force of the wall on your body.
So why do I say it’s friction holding you up?
You notice the walls are made out of a kind of rough, sticky material. What if we took this material away and instead replaced with stainless steel, coated with olive oil? In the ideal Gravitron ride, where the walls are perfectly vertical, you would slide down the walls as quickly as if the ride were not spinning. That is to say, you’d freefall to the ground.
To see why this is, I point you to first panel of Figure 2.
The normal force, which is equivalent to the centripetal force in this case, points perpendicular to gravity. No matter how hard the normal force pushes, it cannot negate gravity. Friction, on the other hand, opposes motion. It only exerts as much force as necessary to stop you from sliding downward. The maximum amount of force friction can exert is proportional to the normal force on an object. That’s why they spin the gravitron, the faster it spins, the more normal force generated, and the more friction between your body and the wall, enough to keep you from falling down.
But a Gravitron does NOT need to spin for the ride to work. A much less exciting way for riders to stick to the walls would be to coat the walls in velcro and ask riders to wear a velcro suit. When the floors drop here, riders will stay in place. Velcro by itself is enough friction to keep a person of average mass suspended. But this approach has two disadvantages. One: the ride is now mass-dependent. Will work for less massive people, will not work for more massive people. Two: kind of takes all the magic out of it, huh.
Figure 2 panel 2 shows an alternative Gravitron configuration. There is a small tilt to the walls which allows normal force to have an upward component. These rides can operate at lower speeds, since friction, in a sense, doesn’t need to do all the work. On the other extreme, it’s conceivable that a Gravitron ride might eliminate the need for friction altogether by delicately balancing the angle of tilt with the speed of rotation. This is not a very safe idea, though. If there is not enough normal force in the horizontal direction to keep riders in circular motion, they will fly out the top of the ride. There are currently no Gravitron rides designed this way that I’m aware of.
In my correspondences with readers, I’ve come across some misconceptions:
- Friction cannot counteract gravity: sure it can! Ever sat on a grassy hill and not slid down to the bottom?
- Centripetal force is able to counteract gravity: in this case, no. By definition the centripetal force points perpendicular to gravity.
- There’s no such thing as friction/centrifugal force is not a fictitious force/gravity is imaginary: whatever you say. you’re getting a little too deep for me.
This was fun. I wish I could do this with all my stories 😦