Why do people do such stupid things? In today's stupid thing, these children decide to use the wheel on a gasoline-powered scooter to spin up a little joy at a park. Oh, don't worry, they have helmets so everything should be fine. NO. Everything is not good. This is why we can't have nice things.
Of course, these people are not the first (or unfortunately the last) to try this stunt. It rarely ends well.
But what makes this so difficult? Why do you want to stay as close to me as possible? Of course, the answer is about physics.
Forces when moving in a circle
It begins with acceleration. If you have an acceleration object, you need a net force on that object. This is the basic model of movement. It looks like this.
Yes, "m" is the object's mass and "a" is the acceleration. But how are the arrows over F and a? The arrow means that these quantities are vectors. Both acceleration and power have directions as well as size. Pressing with a force of 1 Newton (the power unit) on the left differs from pressing 1 N on the right. But if the object accelerates (even a vector) there must be a force.
What is the definition of acceleration? During a short time interval I can define acceleration as follows:
There will be an acceleration when there is a change in speed. This means that an object that accelerates or slows down will accelerate. But wait! How about an object moving in a circle? It's also acceleration. Since the speed is also a vector, only change in the speed direction would also be an acceleration.
The acceleration of an object moving in a circle points to the center of the circle. The faster you increase the acceleration volume. The larger the radius of the circle, the less acceleration. But you already knew this. You can feel yourself accelerating in a turning car. If you take the quick turn too fast, you can really feel it.
However, if we want to talk about the physics of folly running around, the speed cannot be the basic idea to use. If you are on a rotating platform, the size of your speed depends on how far you are from the center of the joy book. A better quantity to consider is the angular velocity. This is a measure of how quickly your angular position changes, and it is the same for any position on a rotating platform (but it can still change over time).
With the angular velocity I get the following expression for the size acceleration for an object moving in a circle.
The angular velocity is ω and the distance from the center of rotation is r. But now we have something important. This means that the longer you are in the middle of the rotating carousel, the greater the acceleration. Also, the greater the acceleration the greater the force required to keep you in place.
Modeling Rotational Force
You know I like to include some type of demonstration to support physics. In this case, I want to show the difference in circular forces for the case where a person is farther from the center of rotation. I have this spinning platform (it is very useful). On the platform I have two lots attached with the rubber band near the middle and one further away. For a rubber band, the greater the force the more it stretches. So, the mass that extends longer has a greater force.
This looks like I have a top mounted camera that rotates with the platform.
If it is not clear that outer mass has a greater distance, I measured it for you. The inner rubber band is 8 cm long (stretched) and the outer is 13 cm.
Estimation of Real Forces
So how about this stupid pleasure hour? How difficult would it be to stick to this thing and not fly? I start with some estimates. Let's say that humans have a mass of 75 kilos and begin at a distance of 15 centimeters from the middle of the merry round.
For maximum angular speed, I can only release this video in Tracker Video Analysis to get a reasonable value of about 7.8 radians per second (74.5 rpm).
You may think I could only use this to calculate the acceleration and then calculate the force. Yes, I can, and I really do. But there is a problem-people take up space. This means that this man does not move in a circle with a radius of 15 cm. Well, part of it does, but other parts of his body have a smaller radius of motion. So, to calculate the acceleration which radius should I use? It is a complicated question (one that I will answer in the future), but as a rough approximation I will only use 15 cm.
The acceleration of this man would be 9.1 m / s 2 which requires a force of 684 Newtons. This is a significant force – especially if you compare it to the guy's weight of 735 Newton. It's like he's hanging from a pole to stay close to the center of the circle. But if he stumbles, just a little, bad things will happen. If his radius increases by only 5 cm, the necessary force jumps up to 912 Newton. The next thing you know, he's flying away from the joy and he's not so happy.
But it's still a super stupid idea. Even if you know that it is possible to spin in a circle, you will be better off doing something else.
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