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..

 

[member 553083]

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.