Without friction and other forces including that of gravity, the ball will continue rolling with the same velocity unless it hits something or someone kicks it.
Understanding the concept of a net external force is crucial in understanding Newton's first law. To illustrate this, consider a rope being used in a tug of war. There are two opposing forces in the activity but if the two sides pull with the same force then the rope would not move. That is, the two forces cancel each other out resulting to no net force on the rope. Thus, forces may be acting on an object but they are applied in such a manner that they cancel each other's effects. Force is a vector so it is important to take account of the direction. The result is that there will be no change in velocity since Force, F = 0. In calculus, this would be represented as dv/dt = 0 when F = 0 or simply, there is no differential change in velocity when there is no net external force. This is illustrated in the following;
Figure 1. A Physics book pulled downward by gravity but the table exerts an upward push. The book does not move because the two forces cancel out. Note that the table is an inanimate object but is exerting force. The occurrence of force applied by the table will be explained further in Newton's Third law.
2.0 Newton's Second Law of Motion: Force and its Representation
"The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object."
While the first law describes the behaviour of objects where the F = 0, the second law is concerned with the situation where there is an unbalanced force. If F 0, then dv/dt is 0. In simple terms, the object accelerates, a, the rate of which is equal to the force applied divided the mass of the object. The acceleration of an object produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and is inversely proportional to the mass of the object. In equation form:
Newton's Second Law is used to account for the acceleration of an object and not the motion itself. This law made it possible to quantify the concept of force. Whereas before it was previously defined as a push or pull, force was now quantified using the unit Newton (N). 1 N is equivalent to the force required to impart a 1 kg mass with acceleration of 1 m/s/s. The vector nature of force is also highlighted in the second law and gave rise to the need for constructing free body diagrams (FBDs). A free body diagram is a simple representation of an object with arrows. These arrows represent the forces together with its direction and intensity. In constructing FBDs, it is essential to take full account of all the forces acting on the object including action-at-a-distance force. An illustration of FBDs and unbalanced forces are shown:
Figure 2. The object is acted upon by forces which are unbalanced in all three cases thereby resulting to an acceleration of the body mass.
3.0 Newton's Third Law of Motion: Action- Reaction
"For every action, there is an equal and opposite reaction"