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After calculating the position, velocity and acceleration for the penguin body, I moved onto analyzing the penguin wing. The following diagram will be helpful in this analysis.

Image Added

Figure. Wing-Body Geometry

When the body of the penguin moves up, the wing at the point where it intersects the body has the same velocity and acceleration as the body. Then by simple geometry we can find the angle of the wing as a function of the position of the body. 

Θ_wing=atan((r-y₀)/a)

Then after finding the wing angle, the velocity and acceleration tangent to the wing can be found by more geometric relations.

V_tan,wing=V_body*cos(Θ_wing)

_Atan,wing=A_body*cos(Θ_wing)

After the tangent components are found, the angular velocity and accelerations will be found by the following equations.

w_wing=V_tan,wing/l=V_tan,wing*cos(Θ_wing)/a

_alphawing=A_tan,wing/l=A_tan,wing*cos(Θ_wing)/a

Lastly, the magnitude of the velocity and acceleration of the wing tip can be found by the following relations.

V_wing=w_wing*l_wing

_Awing=alpha_wing*l_wing