Okay, so I got some really great advice from the community here but I am still hung up on some conceptual problems. I posted earlier trying to determine the axis that a bicycle rotates about when doing a wheelie. Since then I have realized that there is not any unique axis in rotational motion, rather axes are better chosen for the convenience of calculation. Here is the diagram of the object of interest:
It shows the frame of a bike and its front tire at the moment that it begins to lift off the ground. As I have chosen the bike as a frame of reference, its acceleration creates fictitious inertial forces in both the x and y direction.
I have chosen the center of mass as having the same position as the axis of rotation in order to easily break down motion into its transnational and rotational components.
I can calculate the moment that the body begins to rotate about its center of mass by summing the torques produced by the normal force on the rear axle and the horizontal applied force on the back of the frame. When the applied force produces a large enough torque there will be an angular acceleration about the center of mass.
What I fail to understand is why the center of mass rises above its initial height. What accelerates the COM to move it above its initial height with respect to the surface it is moving across?