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DISCUSSION and HINTS
In this problem, we desire to relate the rotation rates of the slotted wheel and the disk. With the two rigid bodies connected by a pin-in-slot joint, we are not able to use the rigid body kinematics equations by themselves. Let's discuss that below.

Before we do, however, can you think of a good application for such a mechanism design? Take a look at this short video.
Velocity analysis
Here, we can use the rigid body velocity equation to relate the motions of P and C:
vP = vC + ωdisk x rP/C
However, we cannot use a rigid body velocity equation to relate the motion of points O and P (the reason for this is that O and P are not connected by a rigid body). In its place, we can use the moving reference frame velocity equation with an observer attached to the slotted wheel:
vP = vO + (vP/O)rel + ω x rP/O
where ω is the angular velocity of the observer, and (vP/O)rel is the velocity of P as seen by our observer on the disk. Note that with the observer being attached to the slotted wheel, this observer sees motion of P only along the slot.
Combine these two equations to produce two scalar equations.
Acceleration analysis
We will use the same procedure for acceleration as we did for velocity - use a rigid body equation for the disk and a moving reference frame equation relating O and P:
aP = aC + αdisk x rP/C + ωdisk x (ωdisk x rP/C)
aP = aO + (aP/O)rel + α x rP/O + 2ω x (vP/O)rel + ω x (ω x rP/O)
where α is the angular acceleration of the observer, and (aP/O)rel is the acceleration of P as seen by our observer on the slotted wheel. Again, note that with the observer being attached to the slotted wheel, this observer sees motion of P only along the slot.
Combine these two equations to produce two scalar equations.