If you thought that the reason only one of the wheels comes up in the previous experiment is that there is friction on one side, this addendum is for you: Gyro -> Mechanical Inductor
Qualitative Information: In the experiment, I felt greater resistance when I tried to increase the torque I applied, to turn the wheel sub-assembly horizontal.
This is equivalent to an inductor's behavior - an electrical inductor's voltage response depends on the rate of change of current. I theorized in my blog post (http://relmachine.blogspot.com/2009/06/generalizing-capacitors-and-inductors.html) that the rate of change of current is the equivalent of rate of change of torque. The behavior is consistent with that theory.
(Reference http://en.wikipedia.org/wiki/Inductance paying special attention to the concept of mutual inductance in the section titled 'coupled inductors')
The analysis of the experiment Addendum to Expt:8A proceeds as follows:
The two mechanical inductors in the circuit of the RelMachine have a strong coupling and therefore a very high mutual inductance, M. In fact this mutual inductance is almost equal to the inductance of a single wheel, L. So when one wheel is rotated, the mutual inductance causes a rotation of the other. That's why the second wheel moves when the first is rotated.
Interestingly, L(Total) of the two inductors in the RelMachine = ( L + M(assuming strong coupling, M approaches L))/2 ~ L
i.e. L(Total) ~ L
So the machine only displays half the inductance it contains. Therefore only one wheel is supported in the first part of Experiment 8A.
The situation in the RelMachine at the moment resembles a transformer circuit with a conversion ratio of 1:1. Tuning both sides of this transformer circuit will change the circuit to a band-pass filter of sorts and help refine the RelMachine's frequency-response curve to a sharp high, i.e. allow for resonance when driven by the right power source. The Tesla coil for instance works because of resonance in an electrical circuit with double inductors, coupled like a transformer.
Qualitative Information: In the experiment, I felt greater resistance when I tried to increase the torque I applied, to turn the wheel sub-assembly horizontal.
This is equivalent to an inductor's behavior - an electrical inductor's voltage response depends on the rate of change of current. I theorized in my blog post (http://relmachine.blogspot.com/2009/06/generalizing-capacitors-and-inductors.html) that the rate of change of current is the equivalent of rate of change of torque. The behavior is consistent with that theory.
(Reference http://en.wikipedia.org/wiki/Inductance paying special attention to the concept of mutual inductance in the section titled 'coupled inductors')
The analysis of the experiment Addendum to Expt:8A proceeds as follows:
The two mechanical inductors in the circuit of the RelMachine have a strong coupling and therefore a very high mutual inductance, M. In fact this mutual inductance is almost equal to the inductance of a single wheel, L. So when one wheel is rotated, the mutual inductance causes a rotation of the other. That's why the second wheel moves when the first is rotated.
Interestingly, L(Total) of the two inductors in the RelMachine = ( L + M(assuming strong coupling, M approaches L))/2 ~ L
i.e. L(Total) ~ L
So the machine only displays half the inductance it contains. Therefore only one wheel is supported in the first part of Experiment 8A.
The situation in the RelMachine at the moment resembles a transformer circuit with a conversion ratio of 1:1. Tuning both sides of this transformer circuit will change the circuit to a band-pass filter of sorts and help refine the RelMachine's frequency-response curve to a sharp high, i.e. allow for resonance when driven by the right power source. The Tesla coil for instance works because of resonance in an electrical circuit with double inductors, coupled like a transformer.
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