Re: Experiments do not confirm conservation of angular momentum-
- From: JEMebius <jemebius@xxxxxxxxx>
- Date: Wed, 15 Apr 2009 22:33:55 +0100
franklinhu@xxxxxxxxx wrote:
I had originally proposed the question "Why a skater spins faster as
they close their arms"
http://groups.google.com/group/sci.physics/browse_frm/thread/ddbb56576d9bbf4e/964aa950e7aac5f?q=fhuangular
The answer that came back was that my original theory about how it
rotates faster just because the the mass is trying to maintain the
same linear momentum was wrong because if you reduce the radius by one
half, you should increase the rotation rate by 4 times. I had
predicted an increase of only 2 times.
The math for conservation of angular momentum works out as:
Angular momentum = radius^2 X rate of rotation.
If Angular momentum is constant, a radius of .5 means that rate of
rotation must be 4.
Well, I find this hard to believe that it would rotate 4 times faster
- that just seems way to fast. I never take anything on faith - I do
my own experiments where possible.
So, I setup an experiment to confirm conservation of angular momentum.
You can see this series of experiments on my YouTube video:
http://www.youtube.com/watch?v=A00bedGd-Ig
I created a mechanism with arms which could rotate outwards. As I spin
the mechanism, the arms extend and I tied a string to the arms so I
could pull the arms to reduce the radius of the steel balls attached
to the ends of the arms by one half.
My initial experiment started with a radius of 5 inches with a
rotational speed of .93 RPS (rotations per second). When the radius
was reduced to 2.5 inches, the rotational speed increased to only to
1.57 rps. This is far, far less than what convservation of angular
momentum predicts which should have been close to 3.75 rps.
My initial reaction was that this couldn't be right and that the mass
of the rotating mechanism must be slowing the rotation rate
considerably. So to compensate, I increased the weights on the arms
nearly 6 times so that the mass of the mechanism was 7 oz compared to
the mass of the weights on the arms which was 12.5 oz (versus 2 oz
before). I was expecting to see some different results.
Much to my surprise, the results came back nearly identical to the
first experiment with nearly identical rotation rates. It seemed that
it didn't matter what size mass I placed on the arms. I wonder if I
put a bowling ball on th ends of the arms if I'd get the same results
again! Still much, much slower than conservation of angular momentum
would predict.
So, I figured, I need to reduce the mass of the rotating mass to
almost nothing. To do this, I created a 3rd experiment where I just
swung a weight attached to a string around in a circle. I pull the
string to decrease the radius by one half. Surely, in this situation,
the mass of the mechanism is zero. I am also spinning the weight fast
enough that it is nearly horizontal during the entire experiment which
should counteract any effect that gravity might have on changing the
orientation of the weight.
The result was when starting out with R=12 inches, the measured
rotation rate was 2.3 rps. When the string was pulled in to reduce R=6
inches, the rotations increased to only 3.33 rps. Clearly, it rotates
faster, but nowhere near the predicted 4x rotation of 9.2 rpm. There
is clearly still frictional effects slowing down the result, but this
is only 1.4 times faster and the experiment is done quickly enough to
discount most of the effects from friction.
I also looked at an experiment done on the international space
station. Surely, this eliminates gravitational and frictional effects.
I made estimates of the radius of the device from the original video
which starts out with R=2.75 with a 1.03 rpm and ends with R=1 with a
2.5 rpm. The angular momentum formula would predict a final rotation
rate of 7.8 rpm. Once again falling far short of prediction.
The resutls from real experiments are far closer to my original
prediction that the rotation rate would double, not quadruple. If the
experiment got over double the rotation, I could believe that my
original prediction was wrong and that the true final rotation rate
could have been 4 times, but it even wasn't close.
Because of these results, I challenge anyone to show me an experiment
which actually does show a quadrupling of rotation speed when the
radius is reduced by half. I was unable to find any such experiments
on my search of the web, and I seriously doubt that anyone can find
such an experiment being performed ever!
I think it may even be possible that the formula for conservation of
angular momentum may be wrong. Have you ever personally experimentally
confirmed the conservation of angular momentum formula or even know of
anyone first hand that has or had it demonstrated to you? Or, do
believe in the formula just because it was printed in a book, accepted
by scientists universally without a scrap of experimental evidence to
back it up.
I challenge you to find that scrap of evidence. Remember I am
specifically looking for confirmation of angular momentum in an
experiment similar to what I have done. Not conservation of angular
momentum in molecules and atoms that we cannot directly see or any
other such experiment which relies on indirect observation.
-fhuangular
Key concept in actual experimentation is the radius of gyration.
See for instance http://en.wikipedia.org/wiki/Radius_of_gyration
The radius of gyration of a rigid assembly rotating about a fixed axis is
r = sqrt (J/M),
where J is the moment of inertia with respect to the actual rotation axis, and M is the mass of the rotating assembly.
NOTE: always take for J the total moment of inertia of the object being studied and/or tested and its support =and of course= the rotor of the driving engine, if any engine is present in the experiment. Remark: take into account the gear ratio from engine to object.
From the definition of the radius of gyration it is clear that when it is halved by whatever mechanism the angular speed indeed increases by a factor of four.
One sees: the radius of gyration is a kind of a weighted mean of the distances of the several different parts, molecules and atoms of the object from the axis of rotation.
The radius of gyration equals the actual distance from the axis only if all matter of the object plus support is at a uniform distance from the axis (cylinder mantle and any subset in mathematical sense of the cylinder mantle).
The uniform distance cannot be realised in practice. It can of course be approximated within a few tenths of procents by small objects and thin cylindrical shells.
The conservation of angular momentum may be tested by means of a simple spherical pendulum, just consisting of a small metal ball attached to a thin rope. Put the ball into an (approximately) elliptical motion and observe its maximal and minimal speeds and its minimal and maximal distances from the vertical. A digital camera exactly vertically underneath the suspension and the bob should do the job.
Do not be disappointed if the measurements are 1 - 2 % off the theory. Such is physics and such are measurements.
In my opinion the pendulum experiment is far better than the experiment shown in the video at http://www.youtube.com/watch?v=A00bedGd-Ig , just because it is far simpler.
Good luck: Johan E. Mebius
.
- References:
- Experiments do not confirm conservation of angular momentum
- From: franklinhu
- Experiments do not confirm conservation of angular momentum
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