Spinning gyroscope loses weight?

Question

I ran two tests with a toy gyroscope spinning on a weighing scale that is accurate to $1$mg. The scale was reset to zero before the tests. The gyroscope was flipped over between test $1$ and test $2$. Each test consisted of $100$ weight readings taken over roughly $20$ seconds. The readings changed rapidly so they had to be read by stepping through videos of the experiment.

There was a mean loss of weight of $10\pm 2\ $mg!

I suspended the spinning gyroscope directly over the balance tray to check if there was any downdraft that might influence the results. I didn't measure anything.

Caveat

However I must admit the instructions for the scales say “do not use balance for dynamic weighing” because of errors due to “stability compensation”.

Test 1

Standard Error Calculation

N: 100 M: -0.01 SS: 0.02 s2 = SS/(N - 1) = 0.02/(100-1) = 0 s = √s2 = √0 = 0.02 SE = s/√N = 0.02/√100 = 0

The standard error is 0.00152

Mean: -0.01g +/- 0.002

-0.012 -0.027 -0.019 -0.025 -0.021 0.000 -0.011 0.000 -0.005 -0.013 -0.011 -0.022 -0.015 -0.014 -0.011 -0.005 0.004 -0.005 0.000 -0.013 -0.014 -0.016 -0.011 0.000 -0.006 0.008 0.000 -0.017 -0.007 -0.011 -0.014 0.021 0.008 -0.009 0.005 -0.020 -0.010 -0.005 -0.030 -0.011 -0.006 0.000 -0.005 -0.020 0.000 -0.018 -0.017 -0.011 0.000 -0.019 -0.015 -0.005 0.000 -0.028 0.000 -0.032 -0.033 0.006 -0.023 0.000 -0.004 0.011 -0.026 0.006 0.005 -0.011 -0.003 0.006 0.010 -0.033 0.005 -0.025 0.007 -0.039 0.000 -0.039 -0.012 -0.009 -0.023 -0.003 0.000 -0.055 -0.029 0.000 -0.008 -0.046 0.000 -0.003 -0.007 -0.043 -0.012 0.004 -0.024 -0.008 -0.059 0.006 -0.035 0.027 0.010 -0.027

Test 2

Standard Error Calculation

N: 100 M: -0.01 SS: 0.06 s2 = SS/(N - 1) = 0.06/(100-1) = 0 s = √s2 = √0 = 0.02 SE = s/√N = 0.02/√100 = 0

The standard error is 0.00241

Mean: -0.01g +/- 0.002

-0.015 -0.018 -0.011 -0.015 0.000 -0.004 -0.003 0.007 -0.008 0.011 -0.059 -0.040 -0.012 0.000 0.005 -0.025 -0.026 0.016 0.000 -0.007 0.000 -0.028 -0.013 0.029 -0.031 -0.007 0.003 -0.028 -0.005 0.000 -0.038 -0.007 0.007 0.000 -0.040 0.000 0.013 -0.013 0.015 -0.020 -0.057 -0.011 0.026 -0.064 0.022 -0.052 0.005 -0.039 0.011 -0.042 0.000 -0.034 0.008 -0.040 0.003 -0.043 -0.047 -0.005 -0.003 -0.006 0.016 0.018 0.022 -0.047 0.016 -0.036 0.026 -0.054 0.027 -0.045 -0.055 0.012 -0.056 0.004 -0.039 -0.036 0.000 0.005 -0.047 -0.040 0.024 -0.033 0.024 0.023 -0.037 0.024 -0.018 -0.017 -0.007 0.003 -0.016 0.000 -0.020 -0.010 0.015 -0.008 0.012 0.019 -0.023 0.014

Answer 1

You are substantially overstating the precision of your measurements.

The readings changed rapidly so they had to be read by stepping through videos of the experiment.

What you mean is that you placed an object on a scale and the scale never gave a stable reading at all. So the numbers that you reported are numbers that flickered across the display momentarily over 20 seconds. You repeated this process twice.

Frankly, none of these numbers are good data. The scale is clearly not designed to measure the weight of such a moving object. The dynamic response of the scale is clearly insufficient for what you are doing here. This scale is not "accurate to 1 mg" under these conditions. I suspect that the manufacturer’s documentation would provide explicit guidance against using it in this manner.

However, let's neglect the fact that none of these are good measures.

The data that you have listed as Test 1 has a mean of -0.011 g and a standard deviation of 0.015 g. This is an attempt to measure a single quantity, the mass of the gyroscope. So this is not 100 measurements with an uncertainty of 0.001 g each, but one measurement with an uncertainty of 0.015 g.

Similarly, the data that you have listed as Test 2 has a mean of -0.011 g and a standard deviation of 0.024 g.

In addition to the statistical uncertainty you have an uncertainty due to the measurement device which you report as 0.001 g. This is a separate component of uncertainty from the statistical uncertainty. Since the device is not being used according to the manufacturer’s documentation this is most likely a severe underestimate of this uncertainty*. However, in the spirit of the exercise, let’s take the 0.001 g figure anyway.

To determine the uncertainty of the mean of the measurements we would add the uncertainties in quadrature. So that would give us a standard uncertainty of $$\sqrt{0.5 \ 0.015^2 + 0.5 \ 0.024^2 + 0.001^2}=0.020$$

So with that more correct level of uncertainty, the result is consistent with 0.

*Personally, I would tend to think of the mean of your measurements as actually measuring this uncertainty. We know from physics and other experiments that the actual value is 0. So the difference from zero estimates this uncertainty. Call it 0.010 g non-statistical uncertainty. This would lead to a combined uncertainty of 0.022 g.

Answer 2

One thought as to why you might see this: Is your gyroscope perfectly balanced?

If not, it will generate up and down forces as it spins. At one instant, it will press down harder on the scale and be measured at a higher weight. At another, a lower weight.

You can check on this a couple ways. Do you get less variation in your measurements if the gyroscope isn't spinning? Do you get more consistent results if you average 1000 measurements?

Answer 3

A lot of people have been misled by this apparent effect, notably Eric Laithwaite in his later years¹.

I suggest that you need to be able to collect six-axis data at the point of contact, substantially faster than the revolution speed of the rotor. Ultimately, you will probably need to work in a vacuum.

You will need to approach this with the intention of "balancing the books", i.e. determining that there is no unexplained input of energy. If you consistently have an excess, i.e. the gyro appears lighter over multiple revolutions, then you've possibly found something which would challenge the broader community but even then you should be asking "what have I overlooked" rather than claiming something new.

This furrow really has been ploughed many, many times. By way of comparison, I suggest you review https://en.wikipedia.org/wiki/Pioneer_anomaly which indicates the degree of precision modern physics brings to bear when confronted with something apparently inexplicable.

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¹ https://patents.google.com/patent/US5860317A/en