Why? Because watches are obviously not available, laser devices and light sensors are sold in the market .
Fidget Spinner is a new trend among young people, a descendant of Rubik’s cubes, of 9999in1 video games, of Tamagotchi virtual chickens… You gradually see it appear. everywhere, from the street to every newspaper, you wonder where to buy one to play with because it looks good…
That popularity prompted Rhett Allain, associate professor of physics at Southeastern Louisiana University, to investigate how long the Fidget Spinner (FS) device can rotate? First, Allain shows that the time it takes for the FS to rotate is based on its angular velocity. First, understand basic rotation. For example, if we have an object that rotates around the center of a bicycle wheel (pictured below), we can determine the position of the angle at any point, and call that angle θ.
If this wheel continues to rotate so that the angle θ changes, we can describe the rate of change of angular velocity with the symbol ω. Here is the formula to find the average angular velocity of the wheel:
It looks a lot like the usual constant velocity calculation. But what if the rotating object slows down or speeds up? So the change in angular velocity will be denoted by α, calculated by the following formula:
If we know the initial angular speed of the rotating object and we assume the final rotation speed of the object is 0 radians/second, we get the formula for the rotation time of the object:
Now we need the angular acceleration – assuming it stays fixed as the device slows down. We can calculate the angular acceleration based on the change in angular velocity, although it is not easy to measure. The FS device rotates too fast to be able to rotate (or at least Associate Professor Allain’s high-speed camera is not “genuine” ), so we will use a laser system to measure the change in velocity. corner.
The upper part is the laser emitter, and the lower part is the light sensor.
The basic mode of operation of this system is that the laser light shines down on the light sensor below. As the FS rotates, it blocks the laser light every time the FS’s wing rotates over the beam. The value measured by the light sensor will be the rotation ratio of the FS device.
But this system also has some minor problems. First, the changing speed of light on the light sensor will be different from the rotation speed of the FS, because on this rotating device there are 3 small holes, creating gaps in each rotation that the laser can through. Second, the FS will rotate very quickly and a lot of rounds, the large amount of data obtained will slow down the analysis.
Here is part of the data obtained:
This will be more interesting tricks than numbers and dry calculations. Instead of sitting and analyzing a large data sheet of time and light (the total data is more than 2 minutes, above is the data of 0.15 seconds), Associate Professor Allain will apply the transformation Fourier.
Explanation : The Fourier transform allows us to transform a function or a signal in the time domain into the frequency domain. Since this data is made up of lots of different trigonometric factors (like sines and cosines) with different measures, their amplitudes will be different. The Fourier transform will show us the different amplitudes, so that we can find the frequency of the oscillation.
Taking a small fraction of the laser data, we get the following Fourier transform:
Where the vertical axis is Amplitude and the horizontal axis is frequency (in Hz).
The peak at 20.14 Hz is the swing amplitude of the FS device (at the time of the first measurement). Other nearby spikes are of no concern at the moment. To determine the angular velocity, we simply multiply this frequency by 2π and we get a speed of 126.54 radians/second.
What if we made a Fourier transform for all the light data that lasted more than 2 minutes? We’ll have a big peak and that data won’t help much. Instead, Associate Professor Allain will break down the data piece by piece and figure out the angular speed. By breaking it down, the angular speed is almost a constant. Based on that, we can create a graph of angular velocity:
The slope in the graph is the angular acceleration with a value of -1.346 radians/s^2, and since this data has a stable line, we can have the angular acceleration at all times be almost constant. Then we can figure out how long the device can be rotated.
With an initial angular velocity of 140 radians/second (slightly faster than the data above), the FS should rotate in 104 seconds. If you want to rotate it longer, just rotate it… faster. Double the original speed, you will double the spin time of the Fidget Spinner.
You have a little more useful information there! As useful as the effect of the Fidget Spinner “cure itchiness” device!