Hula hoop period versus diameter

Thursday began with the Mathematics explains the Universe video in the morning session. This was used to segue into the laboratory. Is every physical system mathematical?

Max Tegmark asserts that the universe is not just mathematical, the universe is only mathematical. In some sense one could argue that if Tegmark is correct, that the universe is fundamentally composed of mathematics, then simulation theory cannot be ruled out. Note that simulation theory does not appear to be experimentally testable, hence simulation theory is not a scientific theory. No test, no science.  

However, if the universe is not fundamentally mathematical, then the probability that reality is a simulation has to decrease. 

Noting that physical science studies anything that is a physical system, then under the mathematical universe theory any and all physical systems must be obeying mathematical equations. Even a novel or unusual system. 

This laboratory exercise also provides a form of laboratory practical examination. There is no guidance other than for the students to determine whether the period of a hula hoop is related to the diameter of the hoop. 

The scaffolding for this laboratory is minimal. 

Desmos. Axis labels apply to pink data points and purple line only.

This term the students were not instructed as to which variable should be the independent variable and which should be the dependent variable. In the above chart the diameter was recorded in meters. In class the example on the board was in centimeters. This was the result of the tape measure being marked in centimeters. 

In CGS the slope of the period versus the diameter is up around 184 with the units being cm/s. Note that this is not a linear velocity. Just exactly what this value means remains unclear. 

Many students chose to make the diameter the independent variable and the period the dependent variable, this leads to a slope on the order of 0.0054 s/cm. Some students concluded that the slope being close to zero meant that there was no relationship.  

Whether there is value in not specifying whether to use MKS or CGS, and specifying which variable to use as the independent variable is unclear. 

Rusty led the way with hooping

Measuring the hoop diameter. This term was first term for which the new 300 meter tape measures were available.

Mary-Ellen learned to hoop during class


Hoop period in seconds versus hoop diameter in meters. The 1.84 slope is in units of meters per second but what, if anything, is moving at that relatively constant speed is unclear. Perhaps the outermost edge of the hoop is moving at relatively constant speed? A smaller hoop has to rotate faster for the outer edge to move as fast as a larger hoop? 

Spreadsheet

Estimating the rim velocity using 2𝜋r÷T or 𝜋d÷T and graphing against the period suggests slightly decreasing rim velocity with increasing period. Of course this overly simplistic approach ignores consideration of centripetal acceleration, centripetal force, and the mass of the hoop. 

Desmos

Hoop period versus the estimated centripetal acceleration at the outer rim appears to be non-linear. Whether this is hyperbolic is not known. 


A video of both the hooping laboratory and the site swap laboratory.

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