Merry-Go-Round, Outside Thimann Labs

Contributed by George Brown

“Why do we think the pseudo-forces are so important that we have a merry-go-round on campus and I’ve even made a simulation of it in the lab room?”

In Conversation With George Brown

I came to UC Santa Cruz in 1991 and the merry-go-round was already here. It is my understanding that it was established in the late 1960s or early 1970s by the early physics faculty. I think it might have been motivated in part through the proximity of the Boardwalk and all the rides that you can experience there that are mindboggling explorations of physics. I’m guessing that those rides led to the creation of miniature version of the merry-go-round here. The hand-operated merry-go-round is, after all, a beautiful way to demonstrate what we call pseudo-Force: the apparent forces that you feel on a reference frame that is either rotating or accelerating in some other way.

The physics behind the merry-go-round experiments are this: if you are in a reference frame that is not accelerating, what we call an ‘inertial reference frame,’ then objects behave normally and travel in a straight line without accelerating or decelerating. But, if you happen to be located in a frame of reference that is either accelerating or rotating, there are apparent forces acting on you. Anyone who has been on merry-go-round could tell you this. These are what we call pseudo-forces.

There are two principal kinds of pseudo-forces that we experience in a rotating reference frame. One is called the centrifugal pseudo-force – that’s the easier one. So, one of the first experiments we have students do is get on the merry-go-round and we spin it, and if they pretend that their reference frame is the merry-go-round, ignoring the redwood trees that appear to be spinning around them, they feel an outward force. The students notice that the force increases as you go further from the center of the merry-go-round, in fact, at the center, you don’t feel any force at all, and they notice the force increases very rapidly with the speed of the merry-go-round. This is the centrifugal pseudo-force, and the students get a visceral feel of it on the merry-go-round.

The centrifugal pseudo-force is a pseudo-force because it is not one of the canonical forces. It’s not the gravitational force, the electric force, the magnetic force, the force of friction, or the force of tension; these forces are evident no matter what you are doing. But this is an apparent force that depends only on your motion and not on charges or gravitational masses yet acts as a force.

The slightly more complicated experiment we do with the merry-go-round is about the Coriolis pseudo-force. For this experiment, we have two students on the merry-go-round, and one student tosses a beanbag to the other student. The students pretend they are on a stationary frame and not moving. But, something weird happens when they toss the beanbag, the beanbag curves in respect to the frame of reference. The students that aren’t on the merry-go-round see the beanbag move in a line- or rather, on a plane. You can launch the beanbag from the ground. The people on the merry-go-round see it curve; the people on the ground see it move along a plane. It is undeniable.

Newton’s first law says that an object is supposed to travel in a straight line without changing its speed; yet, here the object travels in a curved path. If we could put a wall around the reference frame, around the merry-go-round, and you could not see the stationary reference frame around you, you wouldn’t even know you were moving. But, you could plot out the course of the beanbag, and it would be a curve. So, this means either Newton is wrong or you are not in an inertial reference frame. If we are not on an inertial reference frame, we have to fudge Newton’s laws to account for the rotating reference frame. We have to invent these pseudo-forces to determine what is taking an object and forcing it into a curved path. The Coriolis pseudo-force is how we explain the motion of the object relative to the reference frame.

You’ll notice there is a tent over the merry-go-round. We do labs from 8:30 in the morning until 10 o’clock at night, and we never cancel this lab, not for rain or darkness. In fact, since I have been the professor of record for the introductory physics course, I have rewritten the lab manual to expand these experiments. To introduce what we are learning through the merry-go-round experiments, in the laboratory room I’ve made a rotating table by taking a cafeteria table that is round and putting it on a smooth bearing. This allows students to observe the trajectory of objects on a rotating reference frame in another way.

We have pendulum set up on the table. When the table is not rotating, the pendulum appears static – the bob is vertical. When you rotate the table, the pendulum is tilted. We have a doll that sits on the table as the observer, and from the doll’s perspective, the pendulum is no longer vertical. It is like the Mystery Spot! It’s the mystery reference frame! Because for the doll, the pendulum is not vertical, we have to invent the centrifugal pseudo-force. And then, we make the pendulum swing. For the observers in the room, it is moving north to south. But, for the doll, it’s executing a cloverleaf pattern. This is how we demonstrate the Coriolis pseudo-force. We give them the math as well, and it’s hard math, which many students struggle with. But, between the merry-go-round and the table experiments, we make sure the students internalize the idea that sometimes Newton’s Law’s need to be patched up.

Now, why is this important? Why do we think the pseudo-forces are so important that we have a merry-go-round on campus and I’ve even made a simulation of it in the lab room? Earth is a rotating reference frame. So, if we are studying phenomena on Earth, we have no choice but to attend to these pseudo-forces. We have to account for a rotating, accelerating reference frame. The Coriolis pseudo-force is the force responsible for the circular motions of the ocean currents above and below the equator. It’s why they go in opposite directions. As an ocean current moves, it senses the pseudo-forces and moves accordingly. The atmosphere also has global rotational patterns that are due to the pseudo-force the air molecules are experiencing.