## What If a Gear Turns at the Speed of Light… ??

I’m not sure where I came across the question above, but I found it sifting through the images on my computer and it got me to thinking.  If gear 1 turns at the speed of light, I’d be inclined to think gear 2 would turn at 2.5 times the speed of light.  BUT, if the speed of light is the maximum attainable speed of anything, it would stand to reason that gear 2 would turn at the speed of light, which becomes a little bit of a brain teaser.

I took this question around the engineering department at EXAIR and we had some back and forth about it amongst ourselves.  The responses ranged from “It will travel through time”, to “Are these gears RoHS compliant?”, to “Regardless of how fast it spins, those gears are going to need some serious suspension to make it through the desert next year“, and “I’ll bet Han Solo knows”.

Ultimately, we decided that if gear 1 is turning at the speed of light, and accepting that the speed of light is the angular velocity of the gear, gear 2 must also turn at the speed of light.  There can be no difference in the angular velocity from gear 1 to gear 2, otherwise the teeth will shred.  This means that they will both have an angular velocity equal to the speed of light, but gear 2 will have 2.5 times the revolutions in order to do so (compared to gear 1).

Also, for reference, Professor Penurious was pretty sure he’d seen the answer to this on Star Trek at some point.

This was a fun exercise for us in the engineering department and although it doesn’t solve a customer’s problem, it does highlight the type of team all our customers get access to when working with our Application Engineers.

If you have a need for EXAIR products, even a hypothetical one, give us a call.

Lee Evans
Application Engineer
LeeEvans@EXAIR.com
@EXAIR_LE