Re: [Phys-L] no spin decay

[David Bowman <David_Bowman@georgetowncollege.edu>]

Regarding BC's comment:

> No result from spin decay p. 384 current “The Physics Teacher”.
> [1]
>
> or bc incompetent.  
>
> p.s He suspects no data, so can’t verify suspicion not linear
> decay, so will be forced to purchase spinner, and use MicroSet
> to determine dissipation detail.  
>
> [1]  tinyurl.com/WS-SpinDecay

I haven't tried matching the data in the video, or tired the experiment myself with a real spinner.  But if one wants to verify or test for an exponential decay the time honored way is to plot the logarithm of the speed (or frequency) vs. time (or equivalently, make a semi-log-scaled graph).  If the graph is adequately represented as a straight line then the decay is exponential, and the intercept gives the logarithm of the initial speed/frequency, while the negative of the slope gives the decay rate.

OTOH, if one wants to test for or verify a quadratic velocity dissipative decay, the time honored way is to plot the *reciprocal* of the speed (or frequency) vs time.  If the dissipative forces are quadratic in the velocity the plot will again be a straight line with the intercept giving the reciprocal of the initial speed and the slope giving the quadratic decay constant.

OTTH, if one doesn't want to test for or model any particular underlying decay mechanism/model, but just wants mathematically represent how the decay happens one could simply fit the decay curve directly using an appropriately parameterized fitting function.  If the family of fitting functions accurately models the decay over the time range measured the best fit will be good, and the resulting parametrization will adequately characterize the decay.  If the best fit over the whole fitting parameter space is not very good then one knows the family of parameterized curves was badly chosen.  If a wide range of nearly equivalent fitting values do equally well in nicely fitting the decay, then the family of fitting functions has an unnecessary excess of adjustable parameters whose variations are not very independent.

David Bowman