A googol-to-one gear ratio [video] • Hacker News Board

Re: A googol-to-one gear ratio [video]

#61

Post by gizmo686 » Sat, Mar 07, 2020, 2:19 AM UTC

I ran the numbers for going in the other direction.

Suppose that:

    * The 99 slower gears are massless.
    * the fastest gear weighs 10 grams
    * The fastest gear is a cylinder of radius of 2cm
    * The slowest gear completes 1 rotation every 3 days.
    * Relativity only applies when I want it to.

We have:

    * The fastest gear has an angular velocity of:
         w=10^95 radians/second = 10^95 s^-1 //Since radians are unitless
    * The fastest gear has a moment of intertia given by:
        I=mr^2 / 2 = 10^-2 * 4*10^-4 / 2 kg*m^2
    * The fastest gear has a rotational energy of:
        E=Iw^2 / 2= 10^-2 * 4*10^-4 / 2 kg*m^2 *  10^190 s^-2 / 2
        E =  10^184 kg*m^2*s^-2
     * Ignoring all of relativity except E=mc^2, we have
        m = E/c^2
        m ~ 10^184 kg*m^2*s^-2 / 10 ^ 17 m^2*s^2
        m ~ 10^167 kg
    * Acknowledging more of relativity now, we have:
      Schwarzschild radius = 2Gm / c^2
      Schwarzschild radius ~ 10^-12 m^3*kg^-1*s^-2 * 10^167 kg * 10^-17 m^-2*s^2
      Schwarzschild radius ~ 10^138 m

Giving us a black hole large enough to fit about 112 googol observable universes.

I'm sure that I'm missing some relativistic effects here, but I don't even know how to begin to approach that.

Re: A googol-to-one gear ratio [video]

#62

Post by [deleted] » Sat, Mar 07, 2020, 2:19 AM UTC

lacker wrote: post #11

If every electron in the universe came over and cranked that first gear around a hundred times, it still wouldn't be enough to make the last gear visibly move.

[deleted]

Re: A googol-to-one gear ratio [video]

#63

Post by bilekas » Sat, Mar 07, 2020, 2:53 AM UTC

elihu wrote: post #52

bilekas wrote: post #43

This is insane. My OCD is tempered and my love for all things mechanical has been re-ignited. I am curious how this ratio is calculated though, I didn't drill into the relative ratios.. If anyone has a link I would love to see!

It's pretty simple: for each pair of gears that mesh with each other, one has ten times as many teeth as the other, which gives a ten to one reduction. If you chain 100 such reductions, you get 10^100 to one reduction.

But the construction of it ??! It's one thing to put the numbers down, we know they round out nicely, but in my head this needs a very minute level of construct engineering..

For example: If 1 gear(cog?) is 1/1000 of a cm out, would that not effect the ratio over this 'distance' ?

Edit: I might just sound like an idiot right now, but when we get down (or up) to these numbers, i can't help but feel manufacturing numbers play a bigger role

Re: A googol-to-one gear ratio [video]

#64

Post by 6nf » Sat, Mar 07, 2020, 3:23 AM UTC

amelius wrote: post #56

jagged-chisel wrote: post #30

Earlier quoted context omitted.

When all the slack has been rotated out, it would require a tremendous amount of force to rotate that last gear in reverse. After all, the system wants to amplify the gear speed from that end.

Yeah, but if you'd actually run the machine long enough it would simply destroy itself due to the force multiplier.

Sure but the point is that ‘long enough’ in this case is so long that we would never actually see it happen.

Re: A googol-to-one gear ratio [video]

#65

Post by 6nf » Sat, Mar 07, 2020, 3:30 AM UTC

Thorentis wrote: post #3

Why can't it spin faster?

It will just wear out faster

Re: A googol-to-one gear ratio [video]

#66

Post by mkagenius » Sat, Mar 07, 2020, 3:57 AM UTC

bilekas wrote: post #63

elihu wrote: post #52

Earlier quoted context omitted.

It's pretty simple: for each pair of gears that mesh with each other, one has ten times as many teeth as the other, which gives a ten to one reduction. If you chain 100 such reductions, you get 10^100 to one reduction.

But the construction of it ??! It's one thing to put the numbers down, we know they round out nicely, but in my head this needs a very minute level of construct engineering.. For example: If 1 gear(cog?) is 1/1000 of a cm out, would that not effect the ratio over this 'distance' ? Edit: I might just sound like an idiot right now, but when we get down (or up) to these numbers, i can't help but feel manufacturing numbe…

As in the video, they just reuse the same ratio gears in cascade?

Re: A googol-to-one gear ratio [video]

#67

Post by mkagenius » Sat, Mar 07, 2020, 4:01 AM UTC

chrisseaton wrote: post #4

Thorentis wrote: post #3

Why can't it spin faster?

I'm sure it can spin a bit faster. Why can't it spin so fast that the final wheel visibly turns? Well the first wheels would melt from friction or be torn apart before then, and where are you going to get that much energy to turn them so fast? At some point there's the speed of light as a limit as well.

> At some point there's the speed of light as a limit as well.

Why not put it in a dark room before starting up

Re: A googol-to-one gear ratio [video]

#68

Post by pmorais » Sat, Mar 07, 2020, 4:02 AM UTC

nostrademons wrote: post #19

_underfl0w_ wrote: post #8

Part of me likes to thing something crazy would happen if you turned it from the other end. Turn one gear once and the gear at the far other end turns a googol times but melts somewhere around a trillion rotations. Almost doesn't feel too outlandish given a scope that already includes "more energy than the entire known universe has" (per the article) for a measurement.

You would need a tremendous amount of torque to move the last gear, because gears multiply the angular velocity on one side and multiply the torque on the other. If it took one newton-meter (about the weight of one apple on a lever a meter away from the gear) to move the first gear, it would take a googol newton-meters applied at the other end of the device.

It’s actually much worse than that because of reflected inertia. The inertia of the first gear as seen from the last gear is proportional to the square of the gear ratio

Re: A googol-to-one gear ratio [video]

#69

Post by perl4ever » Sat, Mar 07, 2020, 4:02 AM UTC

thedance wrote: post #22

Thorentis wrote: post #3

Why can't it spin faster?

Even if the first gear's teeth were moving at supersonic speeds, there still would not be any perceptible motion of the last 90 gears or so. If the first gear's teeth were moving at relativistic speeds, there would still be no apparent motion in about 80 of the gears. The speed of light is only about a million times higher than the speed of sound, and this contraption loses a factor of a million after six gears.

I did not know this, but according to what I was just reading, pretty much any physical material must rupture when it spins close to the speed of sound in that material.

If you imagine a relativistic spinning disk anyway, then it gets interesting because due to length contraction, the circumference changes relative to the diameter. I'm not up to the math, but it seems like it might change the effective gear ratio depending on your perspective and the closeness of the speed to C.

https://en.wikipedia.org/wiki/Ehrenfest_paradox

Re: A googol-to-one gear ratio [video]

#70

Post by taneq » Sat, Mar 07, 2020, 4:15 AM UTC

warent wrote: post #13

_underfl0w_ wrote: post #8

Part of me likes to thing something crazy would happen if you turned it from the other end. Turn one gear once and the gear at the far other end turns a googol times but melts somewhere around a trillion rotations. Almost doesn't feel too outlandish given a scope that already includes "more energy than the entire known universe has" (per the article) for a measurement.

All this time we've been fussing about clean energy and perpetual motion machines when all we needed was this machine to apply essentially infinite leverage and generate a universe of energy at the flick of the wrist

Step 1 is have a universe's worth of energy in your wrist. ;)