It seems crazy videos like this are becoming more popular.
What a great idea. If you can't spin a merry go round just with your feet, put your scooter on it. Merry go rounds are on their way out of parks anyway. This will just hasten their unfortunate demise (although I can spin any more now that I am older). Just to be clear, don't do this stunt.
I noticed that most of the videos end with a person flying off the merry go round. So, the question: how hard is it to hang on? How fast do these things spin anyway?
Fake Forces Primer
What is a fake force and why is it useful in this case? First, think about a force. A force is an interaction between two objects. You know, like the Earth and me pulling on each other. Or a magnet and a iron nail pulling on each other. And what does a force do to an object? A net force changes the momentum of that object. Most people call this "Newton's Second Law" and it could be written as:
Pretty straight forward. If an object changes it's motion (change in momentum), then there must be a force on that object exerted from some other object. This only works if the reference frame you are in is not itself accelerating. So, that won't work for the spinning wheel of death that we have here. If you are a person sitting on the merry go round, you are at the very least changing the direction of your momentum - so an accelerating reference frame.
And this is where fake forces come in. Fake forces are not interactions between two objects. Instead, they are make believe forces that we need in order to make objects in an accelerating frame behave as though they were in a non-accelerating frame. Fake forces let us use Newtonian mechanics in a place where it doesn't really work.
Everyone has experienced these fake forces. Here you are. In a moving car. The car turns to the left and what happens? You get pushed to the right side of the car. Now, what force was it that pushed you? Or better yet, what object interacted with you? Surprise, there was no object pushing you that way. You want to say there is a force even when there isn't one. This is the essence of the fake force.
In general, the fake force can be written as:
For the case of the merry go round of death, the acceleration of the person's personal frame is toward the center of the merry go round (as is true with the acceleration of all things moving in a circle). This means the fake force would be pointed away from the center of the circle. People call this particular fake force the centrifugal force.
How Fast Does It Spin?
In order to get an estimate of the fake forces acting on these spinning fools, I need to know how fast the stuff was spinning. Using the above video and Tracker Video Analysis, I can plot the horizontal position of one of these guys. Here is what I get for the last part of the motion.
From this, I get a period of about 0.74 seconds. This gives an angular velocity (ω) of 8.49 rad/sec. Does this value seem reasonable? Let me estimate the diameter of the merry go round at about 1.5 m - 2 m (or how about 1.75 meters). This would mean that the linear velocity of a point on the edge would be:
16 mph seems like a plausible speed for a scooter. I am happy enough to move on.
Why do I need the angular velocity anyway? The faster the merry go round spins, the greater the acceleration. The magnitude of the acceleration for a point on the spinning merry go round would be:
Here, r is the radius of the circular motion. So with a radius of 0.875 meters, this would put the acceleration of the person's frame at:
So, Why Does He Fly Out?
Let me draw a force diagram for the guy as he is about to fly out (from his point of view).
If he is going to stay on this merry go round, all of these forces (including the fake one) have to add up to the zero vector. The problem is that as his center of mass moves away from the center of the merry go round, the fake force gets larger. How much larger? Well, the fake force depends on his mass. Suppose he has a mass of 70 kg, then as he changes his radius, the force would look like this.
You can see how things get out of control. These forces are HUGE. His weight is around 700 Newtons. Even at just a radius of 0.5 meters, the fake force is over 2500 Newtons (560 pounds). This is what we (in physics) call as seriously large fake force. When he leans back just a bit, the fake force gets even larger. This causes him to lean back just a bit more and WHAM things get out of control. The next thing he knows he is on the ground.
So how far would he fly? First, he isn't flying. He is falling without style. Ok, so let me assume he has an angular velocity of 8.49 rad/s and the last point he was spinning he has a radius of 1 meter (just a guess for his center of mass). This means that he has a linear velocity (at the time of launch) of 8.49 m/s. Let me assume that he is launched horizontally and with an initial height above the ground of 0.5 meters.
Here we have a pretty standard projectile motion problem. Let me write down the staring values:
In order to solve for the final position (horizontally), I need to first find the time. Since the vertical velocity starts at zero, I can find the time:
Using this time in the x-direction, I can find the final x-position:
Using the above values, I find that they guy will land 2.7 meters (almost 9 feet) away from the merry go round. I bet that hurt.
Let this be a lesson to you would-be-youtube stars. This stunt is a bad idea.
