5.15. What to Remember from Lesson 5#
This has been all about motion without regard to its cause. In a slightly different order from how it was presented, we have a model of constantly accelerated motion (which is an approximation for real-world events).
5.15.1. The speed of a body is proportional to the time elapsed.#
5.15.2. The distance traveled by an object undergoing constant acceleration is proportional to the square of the time elapsed.#
5.15.4. Acceleration near the Earth.#
Galileo’s major contribution to the study of motion was his experiment that showed the above quadratic relation between distance and time. His work focused solely on a particular acceleration, namely that of gravity near the surface of the Earth. That particular value is important enough that it gets its own name, which we affectionately call “little \(g\)”:
In this work he showed that neither the nature of the material nor the mass of a moving object affects these motions.
5.15.5. Projectile motion#
Galileo also demonstrated that an object thrown at an inclination to the Earth’s surface executes a parabolic path with the horizontal component of the object’s velocity unchanging and the vertical component of the object’s velocity decelerating according to \(g\) up and accelerating according to \(g\) down.
5.15.6. Pendulum Motion#
Galileo also found that the frequency that a pendulum repeats back and forth (its period) is independent of how high up the pendulum bob is released and independent of either the mass or material of the pendulum bob. He found that the only quantity that governed this motion is the length of the string. Historically, this has been called Galileo’s Pendulum…law.
5.15.7. What Physics Is#
Each of the above models are approximations to circumstances in which there is no air resistance or friction. This means that these relations tell a story about how things move in an ideal sense. This, Galileo taught us, is the goal of physics: to understand and mathematically model the basic rules of nature in ideal circumstances and then add successive “drops” of reality (like friction or air resistance) depending on the goal of one’s modeling.