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How long would it take a Power Functions M-motor to turn 1 googol times? I have tried figuring it out with a calculator but I was confused.

Michael Verschaeve
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Legofan35664
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    Please edit the question to show what have you tried and where did you get confused. Additionally, if you got to the point of using a calculator, you have probably learned the RPM of the motor, at which point the question is a purely mathematical one, and therefore belongs to another SE site. Nevertheless, I gave below a complete answer according to the "teach a man to fish" philosophy. – zovits Feb 27 '21 at 18:16
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    This is one of those questions where you could literally googol it.... – Robert Columbia Feb 28 '21 at 12:16
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    how long does it take to turn 1 time? multiply that by 1 googol. Elementary school maths, use it! – user253751 Mar 15 '21 at 14:51
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    I tried using a calculator but I couldn’t find one that could multiply by 1 googol – Legofan35664 Mar 16 '21 at 17:18

1 Answers1

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According to Philo's LEGO motor datasheet an unladen PF-M motor rotates with 405 RPM.

One googol is 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (10^100), so the time it takes for an M motor to go this many rotations is (10^100)/405 minutes.

Ordinary calculators usually take a look at such large numbers and throw their hands up, or can't even display them but luckily we have WolframAlpha.

This is 4.695x10^91 years, or about 3.4x10^81 times the current age of the universe. (the Universe is about 14 Gigayears old now, in 2021 :) )

zovits
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  • I suppose the next question would be "What gear ratio would be required to get that number down to just a lifetime?" – Ambo100 Mar 08 '21 at 10:26
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    @Ambo100 1:10^90 would suffice to bring the time down to 46 years and is a nice and round number to work with. The questions of what volume would be occupied by the resulting drivetrain and what torque would be needed to drive it, are left as an exercise to the reader :) – zovits Mar 08 '21 at 10:46