I don't understand why the center of mass' acceleration is equal to 0 when the center of mass should be moving as an external force is exerted on the cue ?
Billiard Balls. Now we can go back and examine the behavior of the billiard balls.Once the cue ball has begun to roll,no net external
force acts on the (twoball) system.Thus, because 0, Eq. 9-14 tells
us that 0 also. Because acceleration is the rate of change of
velocity,we conclude that the velocity of the center of mass of the
system of two balls does not change.When the two balls collide,the
forces that come into play are internal forces,on one ball from the
other. Such forces do not contribute to the net force ,which remains
zero.Thus,the center of mass of the system, which was moving forward
before the collision, must continue to move forward after the
collision,with the same speed and in the same direction.
Best Answer
The external force acts only for the small time when the cue has been struck. Once it moves, there is no force. This means that the ball is moving with zero external force, which means according to Newton's second law, the velocity of the ball is the same. here the act of friction is of less importance as it requires in a billiard play. So the center of mass of the "two-ball" system moves with constant velocity means the acceleration of the center of mass is zero.
On collision, the internal forces acting are equal and opposite. So they will not contribute anything to the net force.