Get Help with Hibbeler Dynamics 20-7 Problem

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The discussion revolves around solving a dynamics problem involving gears, specifically determining the angular velocity of gear A based on the rotation of gear B. Participants express difficulty in starting the problem and achieving the correct vector components in their answers. A suggestion is made to create a sketch to better visualize the problem. One user mentions they have found the answer in the textbook but lacks confidence in their solution method. Clarification and further assistance are requested to ensure understanding of the concepts involved.
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Homework Statement



20-7
If the top gear B rotates at a constant rate of \omega, determine the angular velocity of gear A, which is free to rotate about the shaft and rolls on the bottom fixed gear C.

Homework Equations


V=\omega x r
Va=Vb + \omega x r


The Attempt at a Solution


I'm really having trouble figuring out how to start...I keep getting answers with i (and I know I am doing my cross products right, and I should be getting answers with j and k.
 
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aero10 said:

Homework Statement



20-7
If the top gear B rotates at a constant rate of \omega, determine the angular velocity of gear A, which is free to rotate about the shaft and rolls on the bottom fixed gear C.

Homework Equations


V=\omega x r
Va=Vb + \omega x r


The Attempt at a Solution


I'm really having trouble figuring out how to start...I keep getting answers with i (and I know I am doing my cross products right, and I should be getting answers with j and k.

I think we need a drawing or sketch, before we'll be of much help on this one.

Welcome to the PF, BTW.
 
I got the answer in the back of the book, but I am not confident on the methods by which I got it. So if anyone needs help on this question, I will be able to give concrete reasoning after tomorrow.
 
Thread 'Have I solved this structural engineering equation correctly?'

Thread 'Have I solved this structural engineering equation correctly?'

Hi all, I have a structural engineering book from 1979. I am trying to follow it as best as I can. I have come to a formula that calculates the rotations in radians at the rigid joint that requires an iterative procedure. This equation comes in the form of: $$ x_i = \frac {Q_ih_i + Q_{i+1}h_{i+1}}{4K} + \frac {C}{K}x_{i-1} + \frac {C}{K}x_{i+1} $$ Where: ## Q ## is the horizontal storey shear ## h ## is the storey height ## K = (6G_i + C_i + C_{i+1}) ## ## G = \frac {I_g}{h} ## ## C...
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