Relative Motion Analysis: Acceleration of rotating disk

[_N3WTON_]

Homework Statement

A slotted link AC is is driven by the peg P connected to a rotating disk. Point A is fixed. Determine the link's angular velocity, \omega_{ac} and acceleration, \alpha_{ac} when the angular velocity and acceleration are \omega and \alpha, respectively.
\omega = 6 \frac{rad}{s} CCW
\alpha = 10 \frac{rad}{s^2} CCW
l_{ap} = 0.75 \hspace{1 mm} m
r_{op} = 0.30 \hspace{1 mm} m
\theta = \frac{\pi}{6}

Homework Equations

The Attempt at a Solution

First, I should state that I am genuinely lost on this problem. I am not sure at all how to go about finding the angular velocity for this one. For the acceleration I was thinking that I could perhaps draw an acceleration diagram and attempt to find the solution that way. Maybe I could do something similar for the velocity? I was hoping someone could sort of push me in the right direction/inform me whether there is a better way to solve this rather than a graphical approach. Any help at all is greatly appreciated. Thanks.

 

[Simon Bridge]

The diagram uses theta for two different things... probably because they have the same size at t=0.
Play with the setup for different angles to P ... OP has a constand angular velocity so you can redo the sketch for equal times ans get a feel for what is happening.
There are several approaches but try finding the equation of the angle of the link as a function of time aband differentiating.

 

[_N3WTON_]

The diagram uses theta for two different things... probably because they have the same size at t=0.
Play with the setup for different angles to P ... OP has a constand angular velocity so you can redo the sketch for equal times ans get a feel for what is happening.
There are several approaches but try finding the equation of the angle of the link as a function of time aband differentiating.

Awesome, thanks for the reply. One thought I did have was to consider this as a crank and slotted lever mechanism, where the disk is the crank. Could I do an analysis this way? Or would it be too inaccurate?

 

[Simon Bridge]

Maybe - I'd do it directly by geometry myself.