Well, past Friday I had a Surprise Test and one of the problems was this one, the problem is that I Solved this by a relation of Radius and relative speed.
The variables were:
Wo is an angular velocity that moves against the clock.
The 3 gears have a Radius of 6R, 2R and R.
Wc is 1/6 of Wo
Find Wa(Gear of radius R) and Wb (Gear of radius 2R)
I solved that with something like this:
Since Wo and Wc move against the clock, the relative velocity of Wo compared to Wc comes from: Wo/c = Wo-Wc = 5/6Wo.
Since V =WR
Vo/c=-Va(they can't rotate both against the clock one need to rotate in favor of it)
(5/6Wo)(6R)=-(Wa)(R) Solving this: Wa=-5Wo
Doing the same for Wb but moving in the same direction: Wb= 5/2Wo
The problem is that my teacher said that the speed of Wc didn't matter (but it's the surface where the other gears are rotating) and that you only needed to take the Wo speed and Radius 6, Which is very Stupid in my opinion because if Wc were moving Clock wise the Angular velocity resgitered on Wa and Wb would be greater and I demonstrated it with 3 Gears I had for another class... He called me Stupid that I should stop inventing formulas..... I'm really tired of the bad education I'm having in this stupid university, they Say they are one of the best in Latin America but they are a bunch of pirates (for example a physics teacher saying that gravity was positive when something is going up......).
So, could someone please tell me if I'm wrong and why?