Get Help with Hibbeler Dynamics 20-7 Problem

[aero10]

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.

 

[berkeman]

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.

 

[aero10]

Thank you. Here is a pic of the problem...

http://img12.imageshack.us/img12/9720/dsc00142ya.jpg

Uploaded with ImageShack.us

 

[aero10]

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.

 

[DeeNos]

Hello,
I would suggest breaking down the problem into smaller parts and utilizing the equations listed in the homework statement. First, consider the velocity of gear A, which is free to rotate about the shaft. Using the equation V = ω x r, you can calculate the velocity of gear A based on the angular velocity of gear B and the distance between the two gears. Next, consider the velocity of gear B using the same equation. Then, using the equation Va = Vb + ω x r, you can solve for the angular velocity of gear A. Remember to pay attention to the direction of rotation and use the right-hand rule to determine the direction of the cross product. I hope this helps. Good luck with your problem!