These are my complete notes for Free Fall in Classical Mechanics.
I color-coded my notes according to their meaning - All numbered notes (which I call rules) are red, and include examples and the basis for understanding a topic. Definitions are written in green, and other important information (such as large-scale drawings that are better visualized than explained) was written in blue. All of this information is preserved on this page, with logical flow and breaks. I use ascii line drawings sparingly - If I can convey information or a graph using an image online, I will do so.
All of the knowledge present in these notes are filtered through my personal explanations for them, the result of my attempts to understand and study them from my classes. In the unlikely event there are any egregious errors, contact me at jdlacabe@gmail.com.
Summary of Free Fall (Classical Mechanics)
II. Free Fall.
I.I Intro to Free Fall.
- The only force acting on it is the Force of Gravity.
- It is not touching any other objects.
- There is no air resistance (the object is falling in a vacuum).
# P. Rule 15. ay is the acceleration in the y direction (for free fall on planet earth) is -9.81 m/s², or -g. Thus, free fall is a U.A.M. through the constant acceleration.
g = Acceleration due to Gravity. This is separate from the specific acceleration in the y direction.
gEarth = 9.81 m/s². The acceleration due to gravity on Earth is positive. From a global perspective, the g is not constant at all locations on the planet. However, from a local perspective, the acceleration due to gravity is constant.
For other planets, g is different, like gMars = 3.75 m/s².
# P. Rule 16. Additional facts about gravity:
- 9.81 m/s can also be represented as 9.81 m/s down.
- The acceleration due to gravity, g, is the same no matter the mass of the object.
# Parallax: When the position of an object appears to differ when viewed from different locations.
# P. Rule 17. Sometimes, when you are dealing with an object that changes direction, splitting your calculations into two is necessary in order to find information that serves the equation as a whole: For example, if you were to take a ball and throw it up in the air, catching it in the same y-value that you threw it, the change in position would be 0, making it impossible to find the change in time using the the entirety of the event. Thus, one has to divide the movement of the object along the critical point, with the period of the ball moving upward and then moving down being separately used in calculations. Then, values can be combined to reflect the full event (the change in time, if the ball lands in the same place where it was thrown, would be the change in time of either half of the event doubled, due to symmetry. If the ball lands somewhere elsewhere then it was thrown, then the time for each half would have to be calculated and then added together).
# Common Mistakes in Free Fall:
-When you throw a ball upward, it will not have a positive acceleration. Having such would make it shoot upward like a rocket. Gravity is a positive constant, but the acceleration in the y direction during free fall is -9.81 m/s² for any object, whether moving upward or downward.
-Objects thrown upward do not have an initial velocity of 0 - they already have a positive velocity before being thrown due to whatever is throwing them. An initial velocity of zero in the y direction will not cause an object to move upward - it must be positive.
-The force with which an object is thrown will not effect the acceleration. Regardless of whether a ball is dropped or thrown downward, the acceleration in the y direction will be -9.81 m/s², and only the position and velocity will change to reflect this force.
