When a ball strikes a stick and then bounces back, the stick will recoil to the right. This scenario can be analyzed as a collision. In a collision, two objects apply forces to each other. According to Newton’s third law, these forces are equal and opposite, which ensures that the total momentum of the ball-stick system remains constant. Momentum is defined as the product of an object’s mass and its velocity.
Due to the ball bouncing back, the conservation of momentum dictates that the stick must recoil. Although this hypothetical scenario might not make for exciting viewing in a sports context, it illustrates the principles of what happens at the point of contact or “sweet spot.”
In a situation described as an off-center collision, the stick is brought back to its original position and the ball is launched towards it again. However, this time the ball is aimed at the end of the stick rather than the center. As a result, the stick still recoils to the right but also begins to rotate around its center. This additional motion occurs due to the conservation of angular momentum, which deals with rotational as opposed to linear motion.
While linear momentum depends on an object’s mass and velocity, angular momentum is calculated as the product of an object’s angular velocity and its moment of inertia. The moment of inertia can be thought of as rotational mass, influenced not only by the object’s mass but also by the distribution of that mass. After the collision, the stick gains angular momentum due to its rotation.
Prior to the collision, the stick is not rotating and thus does not possess any angular momentum. For angular momentum to be conserved in this interaction, the ball itself must have angular momentum, even without rotating. The ball acquires angular momentum based on its linear momentum and the point of impact on the stick.
