Dynamics: Angular Acceleration of Rods Connected to Disk

[vercingortix]

Homework Statement

Bars BC and AB and dish OA are attached by a pin like in the picture. The dish has a constant angular velocity \omega\_{0}. Find the angular acceleration of bars BC and AB.

Homework Equations

Relative Motion Equations:
v_{b}=v_{A}+v_{A/B}
a_{B}=a_{A}+\alpha_{A}Xr_{B/A}-\omega^{2}r_{B/A}

The Attempt at a Solution

So far, I have this written down:

V_{A}=\omegar
a_{A}=V_{A}^{2}/r=\omega^{2}r

a_{B}=\alpha_{BC}Xr_{BC}-\omega_{BC}^{2}r_{BC}

Still just fumbling over these equations. Any help is appreciated.

 

[tiny-tim]

welcome to pf!

hi vercingortix! welcome to pf!

(have a theta: θ and an omega: ω )

(centripetal acceleration is irrelevant)

ω = (v_P - v_Q)/PQ

so find v_B as a function of θ ​

 

[vercingortix]

That equation looks foreign to me. What I'm currently trying to do is solve for angular acceleration of the bar by knowing the omega and accelerations of both A & B. Something like the second equation in my original post. I'm very lost.

 

[tiny-tim]

hi vercingortix!

ω = |v_P - v_Q]/PQ

and

α = |a_P - a_Q|/PQ

are the definitions of angular speed and acceleration

so find the x,y components of B as a function of θ, and differentiate to get v_B and a_B ​