Final answer:
Equilibrium during rolling is maintained with no net torque and a constant angular velocity, as seen in rolling without slipping. In heeling, like with boats, equilibrium involves returning to an upright stable position or capsizing in an unstable situation. Rolling equilibrium is influenced by factors such as the object's center of mass acceleration and rotational inertia.
Step-by-step explanation:
How Equilibrium Changes During Rolling and Heeling
When considering rolling motion, we observe that an object may roll without slipping, such as a bicycle wheel or a car tire moving across the pavement. As the object rolls, the point of contact with the ground is momentarily at rest, indicating the presence of static friction, which is essential to avoid slipping. For a rolling object, equilibrium is maintained when there is no net torque and the object moves with a constant angular velocity.
When discussing heeling, often in the context of boats, it refers to the tilt of a vessel due to external forces such as wind or waves. A boat in equilibrium will remain upright, but once it heels, it will either return to its upright position (in the case of a stable equilibrium) or capsize (in an unstable equilibrium).
An example that illustrates the concept of equilibrium is the marble in a bowl. When the bowl is upright, a marble disturbed will oscillate around the stable equilibrium point. In contrast, if the bowl is upside down, and the marble is slightly disturbed, it will not return to the point of equilibrium; this represents an unstable equilibrium point.
The importance of equilibrium in rolling motion is also evident when solving problems involving rolling without slipping, where the acceleration of the center of mass is factored in differently depending on whether an object is sliding or rolling and the object's rotational inertia.