I improved a tiny bit the precision of the tests;
I painted the flywheel of the ball top black, for a slightly more accurate measuring of its angle of tilting, on the white background, (reflections on the brass didn't help).
I centered more precisely the height of the flywheel, so to eliminate whatever residual precession.
I realized that another tiny source of error comes from the camcorder; for these sequences I set the shutter speed at 1/800 second, anyway the image is not recorded all at once, but from above to below, in about 1/80 second. I use a mirror above the spinning top to see it from above, for to know the start and end points of the examined tracks; since I have to move the mirror while the top spins, the image of the top is not always at the same height in the frame; I noticed the problem because, in the video, the mark on the top in the side view appears in a different position than in the view from above, (you can see this if you pause the video).
Now I consider all of this in my calculations.
It may seem boring to repeat continuously the same test, but, by refining the method, and the calculations, the results become more reliable:
I repeated the test considering the margins of maximum error, (minimum and maximum values);
First half Second half
of the track of the track
Measured data:
Track length
mm 239.6-240.0 mm 239.4-239.8Time 0.500-0.504 sec 0.532-0.536 sec
Spin revolutions 33.53-33.63 35.52-35.62
Angle of tilting start 7.0°-7.3° start 6.5°-6.7°*
end 6.5-6.7°* end 5.9°-6.2°
average 6.75°-7.0° average 6.2°-6.45°
Calculated data:
Translational speed 475.4-480.0 mm/sec 446.6-450.8 mm/sec
RPM 4008-4019 3991-4002
Distance traveled
by the ball top
mm 235.7-245.2 mm 229.5-239.4Percentage of slipping -1.7%,+2.2% -4.4%,+0.0%
The results are compatible with the
top not slipping.
* The image of the top on the frame is better focused at halfway across the track, so here the margin of error is reduced from 0.3° to 0.2°.
https://www.youtube.com/watch?v=JWlrLm_Qwr8