After a collision, which factor mainly influences whether an object will roll or slide down an incline?

The factor that mainly influences whether an object will roll or slide down an incline is the moment of inertia. Moment of inertia is a measure of an object's resistance to changes in its rotation about an axis. It depends not only on the mass of the object but also on how that mass is distributed relative to the axis of rotation.

When an object rolls down an incline, its moment of inertia determines how easily it can begin to rotate as it moves down the slope. A larger moment of inertia indicates that the object is more resistant to rolling, which can result in a higher tendency to slide instead. Conversely, if the object has a smaller moment of inertia, it is more likely to roll rather than slide, as it can rotate more easily under the influence of gravitational torque.

While factors like the shape of the object and the incline's surface texture do play roles in the dynamics of the motion, they do not intrinsically determine the rolling versus sliding behavior as fundamentally as the moment of inertia does. The object's mass can affect the gravitational force, but it is the distribution of that mass—reflected in the moment of inertia—that primarily influences rolling and sliding behavior.