Dynamics Question, Planar rigid body/ Relative velocities

[CaityAnn]

http://wps.prenhall.com/wps/media/objects/3076/3149958/studypak/questions/html/Ch16/9e_16_43.html
That is the image of the problem, which includes a solution. PROBLEM- Besides being really confused on their work, the solution they give and the solution in the back of my book are both different! They said Wcd is 15.1 rad/s and my book says 4.03 rad/s, they have the same dimensions and everything.


heres what I am doing, despire the crazy solution given.. I am just trying to get some sort of method and understanding of this stuff, I am taking this course in 5 weeks so its sort of a rush to get it all in..

I want to find Angular velocity of link CD at the instant shown

Vc=Vd+Vc/d ; Vc=Vd+(Wcd x Rcd) Vd won't be moving so it goes to zero
So Vc=(WcdxRcd) ((((So I must need to solve for Vc to get Wcd))))

Va= Vb+ Va/b; Va= Vb + (Wab x Rab), Va won't be moving so it goes to zero
Vb= (Wabx Rab), I can solve for this because I am given Wab and Rab, Vb=18 in/s

Vc=Vb+Vc/d; Vc=Vb+(WcdxRcd) Vc= 8 + (WcdxRcd)
So I just need to find Vc somehow.. On the solution given they do some insane trig that I just don't get, your input is much appreciated so thanks ahead..

 

[Nate810]

The answer is 4.03 rad/s and it can be found by using the equations of motion. You need to solve for the velocity of point B (Vb) which is given. Then you can use the equation Vc=Vb+Vc/d to solve for Wcd, the angular velocity of link CD. Finally, you can use the formula Wcd=Vc/Rcd to calculate the angular velocity.

 

[m2003]

As a scientist, it is important to have a clear understanding of the problem and the solution process before attempting to solve it. In this case, it seems like there may be a discrepancy between the solution given and the one in your textbook. This could be due to different approaches or assumptions made by the authors.

To understand the solution, it may be helpful to break down the problem into smaller components and use basic principles of dynamics to solve it. For example, you could start by finding the velocity of point C relative to point D, using the given information about the velocity of point B and the angular velocity of link AB. Then, using the relative velocity equation, you can find the angular velocity of link CD at the given instant.

It is also important to carefully check your calculations and make sure you are using the correct units and dimensions. Sometimes small errors in calculation can lead to significantly different results. If you are still unsure about the solution, it may be helpful to consult with your instructor or a classmate for clarification.