Problem with Angular velocities
http://i.imgur.com/8uBgB.jpg
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?
Re: Problem with Angular velocities
Well first:
Quote:
(for example a physics teacher saying that gravity was positive when something is going up)......
It really depends on what you designate as "up." If it's easier to set up as positive then you might as well set it up as positive.
Now to the actual problem.
What's the difference between w0 and wc? They both look like the exact same wheel. Until I can better understand it I can't solve it (heck even if I understand it I might not be able to solve it, but it's worth a shot).
I'll give you a tip though, in these sorts of problems the linear velocities of all the gears should be the same.
Re: Problem with Angular velocities
Quote:
So, could someone please tell me if I'm wrong and why?
You're wrong because you're assuming some relations between W0 and Wc that can't be true.
V=rw, as you've already shown you know. So if W0 is 1/6 of Wc, you then KNOW that W0 is measured at a radius R from the centre of the biggest gear... but I'm not really sure why you would need both of them, and frankly, I'm struggling to understand the information you're posting in regards to the question.
Quote:
(for example a physics teacher saying that gravity was positive when something is going up......).
Which is something you can say in physics, because you define directions and therefore which way a value would be to be positive and which would be negative, because most values are gauge invariant and can be defined arbitrarily. Defining upwards as a positive value is the most common definition, so your teacher at the very least not wrong.
Edit: not the first one to rage about this. Darn you Corn!
Re: Problem with Angular velocities
Quote:
Originally Posted by
Lozmaster
You're wrong because you're assuming some relations between W0 and Wc that can't be true.
V=rw, as you've already shown you know. So if W0 is 1/6 of Wc, you then KNOW that W0 is measured at a radius R from the centre of the biggest gear... but I'm not really sure why you would need both of them, and frankly, I'm struggling to understand the information you're posting in regards to the questi
on.
Wo and Wc are different bodies, Wo is the angular velocity of a large metal bar that unite the Gears with radius R and 2R and Wc is the angular velocity of the surface (radius 6R)where the 2 wheels are rotating. To explain what I am thinking let's make it more simple because my english is pretty bad... Let's assume the Bar and the gears A and B are static, if C moves the gears would rotate too right? And if we assume C static and the bar mobile the gears would rotate too, In those cases the wheels would have the same linear velocity of the Surface C and the Bar respectively, making the only difference the radius and the spinning direction.
The Problem is that here we mix Both cases since the Surface is moving at the same direction of the Bar (against clock), one entire cycle of the Gears would take a lot more than if the Surface C were static. If C moved Clock wise and the bar Stayed the same, the cycle of the gears would take less time.
That's why I assume that the Real linear velocity of the wheels is the same as the relative linear velocity between the Bar and the Surface C, Since they are connected by the gears.
Quote:
Originally Posted by
Lozmaster
Which is something you can say in physics, because you define directions and therefore which way a value would be to be positive and which would be negative, because most values are gauge invariant and can be defined arbitrarily. Defining upwards as a positive value is the most common definition, so your teacher at the very least not wrong.
It was a projectile problem, we assumed the start point to be the center and up to be positive and down negative. She said that the the gravity was additive to the initial speed and because of that the projectile was gaining more and more speed to the point it turned out to be infinite when we tried to find the middle point of the trajectory.
In other words when the particle was going up she added the speed generated by the gravity when we assumed that going up was positive and since the gravity pulled the projectile down It should be negative but she only added it and when the results weren't the same as a stupid guide they used, she only said "I don't know why it's wrong and class is over" when we said that gravity should be negative not positive because of the reason above stated.
@Corn; I know that linear Velocities are the same, that's why I used them to make the equations to get the angular speed
