A pitched baseball moves no faster than the pitcher's hand. But a batted ball can move much faster than the bat. What's the difference?

Understanding Newton's First Law of Motion is crucial when examining the flight of a baseball after it's pitched. This law, also known as the law of inertia, states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. In the context of our exercise, once the pitcher releases the baseball, it ideally moves at a constant velocity because the throwing action has set its speed and direction. This is observable in our pitched baseball scenario, where there are no significant external forces like air resistance affecting it, and the ball continues to move at the speed of the pitcher's hand until other forces come into play, such as gravity or the bat.

Improving the trajectory and speed of the pitched ball thus becomes a question of the initial action - how much force the pitcher uses at the point of release. The sudden acceleration of the ball when hit by a bat can also be seen as a direct consequence of this law, as a new external force - the bat - changes the ball's state of motion.

Newton's Third Law of Motion is elegantly demonstrated in the scenario where a bat connects with a baseball. The law postulates that for every action, there is an equal and opposite reaction. As the bat strikes the ball, it applies a force to the ball. Simultaneously, the ball applies an equal and opposite force on the bat. This interaction can be complex, but at its core, it's this mutual force that enables the ball to depart from the bat at great speeds.

The mass of the bat, being significantly larger than that of the ball, contributes to the momentum exchange, letting the ball accelerate more than the bat decelerates. This result is consistent with our understanding of momentum in physics. Hence, the impressive velocities achieved by batted balls are a consequence of both the force applied and the reaction force of the ball, a perfect demonstration of Newton's Third Law.

Momentum is a foundational concept in the physics of baseball that describes the quantity of motion an object possesses. It is fundamentally the product of an object's mass and its velocity. When the pitcher throws the ball, they are transferring momentum from their hand to the ball. Similarly, when a batter hits the ball, there's a transfer of momentum from the bat to the ball, often resulting in a dramatic change in the ball's speed.

The law of conservation of momentum tells us that the total momentum before and after the collision of bat and ball remains constant, assuming no external forces act on the system. While the pitcher's throw and the bat's swing both impart momentum to the ball, the collision process between bat and ball allows for a greater momentum transfer, hence the increase in speed. Understanding this transfer and conservation of momentum is key to analyzing why the ball moves faster after being hit than when it is pitched.

External forces play a significant role in the behavior of objects in motion, such as a baseball. These forces, which include gravity, air resistance, and contact forces like the impact with a bat, can alter an object's speed and direction. In the physics of baseball, recognizing external forces is essential for understanding the full picture of what happens to the ball before, during, and after it's in play.

When the baseball is in flight after being pitched, for simplicity, we often neglect air resistance to focus on the motion imparted by the pitcher's arm. However, in a more detailed analysis, air resistance is an external force that invariably slows the ball down. On the other hand, when the ball is struck by the bat, the force of the bat is an external force that significantly changes the ball’s momentum. Exploring these external forces gives students an in-depth view of the real-world dynamics at play in the game of baseball.