/sci/ - Science & Math

>>11618086
Because with gear multiplication you trade angular speed for torque. So even ignoring the mass of the gears themselves and ignoring losses (which you can't do if you have this many fuckin gears), you could theoretically get whatever speed you desired, but that doesn't mean it would be able to turn a shaft.
>Can a regular Camry engine do 750 mph at 2k rpm in 50th gear
No. It doesn't have enough power.

You've got [eqn] H(s)=\frac{\frac{L}{R}s}{LCs^2+\frac{L}{R}s+1}\ . [/eqn]
The cuttoff is when the power of the output signal is half that of the input. But power is proportional to the square of the amplitude, so half-power occurs when [math] V_o=V_i/\sqrt{2} [/math], which is the same as saying [math]
|H(j\omega)|=2^{-1/2} [/math]. So [eqn] |H(j\omega)|=\frac{L\omega/R}{\sqrt{(1-\omega^2LC)^2+(L\omega/R)^2}}=\frac{1}{\sqrt{2}}\implies\omega_c=\sqrt{\frac{1}{4R^2C^2}+\frac{1}{LC}}-\frac{1}{2RC} [/eqn]
Cutoff is not at resonance.
>>11464962
>but that means current still doesn't flow through the resistor, right?
Why wouldn't it? Impedance is finite. Even at resonance.