2) Tangential remark: This is what modern data looks like. It is
worth showing this data to students, because the format is probably
not what they were expecting.
Back in the bad old days, people used frequency counters, which
would read out the data at fixed intervals, giving the number of
events in each interval. However (!) the modern approach is to
flip that around: rather than points per interval, report the
interval between points. That is to say, timestamp each event,
and report all the timestamps, either as absolute time or as
delta(time).
If necessary, sum the deltas to get the total elapsed time.
The second column (calendar time) does not have enough resolution
to serve as the primary timebase. It provides some supplementary
information, but for basic purposes [e.g. item (3) below] it can
be ignored entirely.
3) Back when I was a sorcerer's apprentice, I was taught that there
are ways of understanding a differential equation that do not
necessarily involve "solving" it in the usual sense, in particular
not necessarily integrating it.
Recommended reference: Apostol _Calculus_
Volume II discusses differential equations.
For example, if you think the frictional force is some function of
velocity, you can write
dv/dt = F(v)
and you can visualize the force law by plotting dv/dt as a function
of v.
It is well worth doing this for the old and new spinner data. For
the data BC got from the web, the plot is here: https://www.av8n.com/physics/img48/fidget-spinner-force-law.png
The red line is a fitted parabola, mostly drag proportional to v^2
but with a small linear component that is noticeable at small v.
For one thing, we notice that the speeds are an order of magnitude
smaller. It appears that the v^2 term (presumably aerodynamic
drag) is not noticeable here. There is a small linear term, plus
a constant term. The constant term goes away at the very smallest
speeds, as it must, since the net force must go to zero at zero
speed.
I do not have a microscopic physical explanation for the constant
term. It will require more thought than I can give it at the moment.
4) The new plot looks noisy.
The untrained human eye is not a good way to analyze noisy data.
It would be nice, from a user-interface point of view, to find
a way to smooth the data ... but that comes later! From a
fundamental physics point of view, the noisy data is the real
data. It carries more information than the smoothed data would,
and I am very happy to see it as-is.
The expert will spend a lot of time and effort looking at the
raw data before deciding how (and whether) to smooth it.