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I was doing my tutorial and given the angular velocity of the first gear, we were required to calculate the angular velocity of the 8th gear given just the no. of teeth for all the gears.

Now I know that there must be a faster way of calculating the angular velocity of the 8th gear then solving for the angular velocity each gear from 1 - 8. (i.e. using the speed ratio formula [itex]\frac{N1}{N2}[/itex] = [itex]\frac{rpm2}{rpm1}[/itex])

**Question 1**: Is there a faster away? (I think there's something like all the gears must move at the same tangential velocity or something right?)

I also noticed that when you multiplied the rpm of each gear by the number of teeth, you get a fixed number (lets call it x) for all the gears. This means that to find the rpm of the 8th gear all I have to do is ([itex]\frac{x}{N8}[/itex].

**Question 2**: What is this relationship? Is it an actual relationship or does it just happen to be a unique thing for the question that I am doing?

Thanks in advance for all your help guys!