How fast can the last cog in a googol machine turn?

On Mar 1, 2020 at 14:52 Daniel de Bruin was a billion seconds old. To celebrate he built a machine that has a gear reduction of one googol (one followed by a hundred zeros) to one

In his words "In order to get the last gear to turn once you'll need to spin the first one a googol amount around. Or better said you'll need more energy than the entire known universe has to do that."

Below is the original video.

https://www.youtube.com/watch?v=nFslB0AcVmM


So it would take more energy than contained in the universe to turn the last gear, but how long (theoretically) would it take?

OK, lets assume that the gears in the actual machine have a radius of  5cm, then the maximum velocity of the first gear would be that at which its outer edge is travelling at (well, just below) the speed of light.

So 0.1*pi gives us approximately 0.31m circumference. So dividing by the speed of light give us 0.31/2.99792×10^8 m/s (meters per second) which mean it will take 0.0000000010 seconds to rotate once. Multiplying by a googol gives us :

3.279×10^83 years  

OK, what is we shrink the googol machine to it smallest size to get in more rotation per second. Lets imagine a the gears are the size of a hydrogen atom. The equation (that I put directly into wolfram alpha) was

(((width of a hydrogen atom in metres)*2*PI/2.99792×10^8)*(10^100))/(seconds in a year)

= 3.3229×10^74 years

And to think, if your immortal you will live to see it happen!