Final answer:
The Center of Mass (COM) of an inverted pendulum model is the highest at the release point or the highest point in its swing when it is momentarily at rest. At this point, gravitational potential energy is at its maximum and kinetic energy is zero.
Step-by-step explanation:
In the context of an inverted pendulum model, the Center of Mass (COM) is the highest when the pendulum is at its highest point in the swing, which is when the pendulum is released from rest. According to the principle of conservation of mechanical energy, the potential energy is at its maximum at the highest point since all the energy is stored as gravitational potential energy. As the pendulum swings down, this potential energy converts into kinetic energy. At the inversion point of the pendulum's swing, where potential energy is at its peak, the rotational kinetic energy is zero as the angular velocity is momentarily zero at this highest point.
When considering a physical pendulum, the torque produced by the gravitational force causes the pendulum to rotate around its pivot point. For small angular displacements, we can use the approximation that sin θ is approximately equal to θ, simplifying the analysis of the motion of the pendulum.