These are my complete notes for Free Fall in Classical Mechanics.
I color-coded my notes according to their meaning - for a complete reference for each type of note, see here (also available in the sidebar). All of the knowledge present in these notes has been filtered through my personal explanations for them, the result of my attempts to understand and study them from my classes and online courses. In the unlikely event there are any egregious errors, contact me at jdlacabe@gmail.com.
Summary of Free Fall (Classical Mechanics)
II. Free Fall.
II.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).
If an object meets all these requirements and is in free fall, then it would have a constant gravitational acceleration relative to the gravitational pull of the planet/celestial object it is on. On Earth for example, the acceleration of all objects in free fall is -9.81 m/s² in the y-direction. See Rule 14 for more information.
#
P. Rule .
Gravitational Acceleration:
gEarth = 9.81 m/s² (when in free fall)
The Acceleration due to Gravity on any planet or space thing is described using the variable 'g'. In and of itself, g cannot be negative as it merely represents an attractive force acting upon an object.
On Earth, for example, the gravitational pull of the planet is described as gEarth = 9.81 m/s². From a global perspective, gEarth is not constant at all locations on the planet. However, from a local perspective, the acceleration due to gravity is constant, and should always be considered as such when solving a problem.
Never accidentally use gEarth for another planet. Other planets/celestial objects have their own gravitational acceleration constants which will likely be given by the problem (or left as an exercise for the reader to determine). For example, gMars = 3.73 m/s².
The acceleration due to gravity, g, is the same no matter the mass of the object. The mass of the planet, however, will alter g as the gravitational pull of the planet will differ.
ay Earth = -9.81 m/s² (when in free fall)
When direction is considered in relation to the gravitational pull, and the xy-plane upon which the object exists is acknowledged (as it will be in practically all Physics problems), then the downward gravitational pull towards the center of the planet will produce a negative acceleration relative to the object's plane (when in free fall).
Thus, ay, the Acceleration due to Gravity in the Y-direction (for free fall on planet earth), is -9.81 m/s², or -g. Note that this can also be represented as 9.81 m/s² Down, but NEVER as -9.81 m/s² Down (which is in effect 9.81 m/s² Up, or reverse gravity).
No matter the positioning of the object (if its tilted or not), the acceleration due to gravity will remain pointed directly downward towards the center of the planet/celestial body. Additionally, note that gravitational force (the force causing the acceleration), which will be described in Section VI, is also always pointed directly downward towards the center of the planet regardless of whether the object is tilted or not; See Rule 60.
The Acceleration due to Gravity must not be confused with the Acceleration due to Gravity in the Y-direction. In practice, the former, g alone (without the negative), will be used much more often in Physics problems, especially when performing free-body problems involving the force of gravity (discussed later on in Subsection VI.II).
g = Acceleration due to Gravity.
ay = Acceleration due to Gravity in the Y-direction.
gEarth = 9.81 m/s². (when in free fall)
ay Earth = -9.81 m/s² (when in free fall)
gEarth = 9.81 m/s² (when in free fall)
The Acceleration due to Gravity on any planet or space thing is described using the variable 'g'. In and of itself, g cannot be negative as it merely represents an attractive force acting upon an object.
On Earth, for example, the gravitational pull of the planet is described as gEarth = 9.81 m/s². From a global perspective, gEarth is not constant at all locations on the planet. However, from a local perspective, the acceleration due to gravity is constant, and should always be considered as such when solving a problem.
Never accidentally use gEarth for another planet. Other planets/celestial objects have their own gravitational acceleration constants which will likely be given by the problem (or left as an exercise for the reader to determine). For example, gMars = 3.73 m/s².
The acceleration due to gravity, g, is the same no matter the mass of the object. The mass of the planet, however, will alter g as the gravitational pull of the planet will differ.
ay Earth = -9.81 m/s² (when in free fall)
When direction is considered in relation to the gravitational pull, and the xy-plane upon which the object exists is acknowledged (as it will be in practically all Physics problems), then the downward gravitational pull towards the center of the planet will produce a negative acceleration relative to the object's plane (when in free fall).
Thus, ay, the Acceleration due to Gravity in the Y-direction (for free fall on planet earth), is -9.81 m/s², or -g. Note that this can also be represented as 9.81 m/s² Down, but NEVER as -9.81 m/s² Down (which is in effect 9.81 m/s² Up, or reverse gravity).
No matter the positioning of the object (if its tilted or not), the acceleration due to gravity will remain pointed directly downward towards the center of the planet/celestial body. Additionally, note that gravitational force (the force causing the acceleration), which will be described in Section VI, is also always pointed directly downward towards the center of the planet regardless of whether the object is tilted or not; See Rule 60.
The Acceleration due to Gravity must not be confused with the Acceleration due to Gravity in the Y-direction. In practice, the former, g alone (without the negative), will be used much more often in Physics problems, especially when performing free-body problems involving the force of gravity (discussed later on in Subsection VI.II).
g = Acceleration due to Gravity.
ay = Acceleration due to Gravity in the Y-direction.
gEarth = 9.81 m/s². (when in free fall)
ay Earth = -9.81 m/s² (when in free fall)
#
P. Rule .
Splitting U.A.M. Calculations:
Sometimes, when you are dealing with an object in free fall that changes direction (such as when gravity pulls down an upward initially thrown upward), splitting your calculations into two parts (or more!) is necessary in order to find information that serves the problem as a whole.
For example, if you were to take a ball and throw it up in the air, catching it at 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 entirety of the event. Thus, one has to split the movement of the object into the periods before and after it passed the critical point (the point mid-air in which the ball stops moving upward and effectively pauses for a moment before it begins falling), with the period of the ball moving upward and the period of it falling downward being dealt with separately in calculations (different U.A.M. sessions as it were, which may share some variables but represent different periods of movement).
After separation, the values from the different sessions can be stitched together to provide a more complete view of the entire movement sequence of the object. The total change in time for the example event, 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 other than where it was thrown, then the time for each half would have to be calculated and then added together to find the total time.
Sometimes, when you are dealing with an object in free fall that changes direction (such as when gravity pulls down an upward initially thrown upward), splitting your calculations into two parts (or more!) is necessary in order to find information that serves the problem as a whole.
For example, if you were to take a ball and throw it up in the air, catching it at 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 entirety of the event. Thus, one has to split the movement of the object into the periods before and after it passed the critical point (the point mid-air in which the ball stops moving upward and effectively pauses for a moment before it begins falling), with the period of the ball moving upward and the period of it falling downward being dealt with separately in calculations (different U.A.M. sessions as it were, which may share some variables but represent different periods of movement).
After separation, the values from the different sessions can be stitched together to provide a more complete view of the entire movement sequence of the object. The total change in time for the example event, 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 other than where it was thrown, then the time for each half would have to be calculated and then added together to find the total time.
# Common Mistakes in Free Fall:
1. When you throw a ball upward, that does not mean that it will 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, regardless of whether it is moving upward or downward (and if it is moving upward in free fall, it is sure as hell to start moving downward soon thereafter!). See Rule 14 for more information regarding gravitational acceleration.
2. Objects thrown upward do not have an initial velocity of 0 (atleast in the y-direction) - they already have a positive velocity before being thrown due to the force applied by whatever is throwing them. An initial velocity of zero in the y-direction will not cause an object to move upward - the initial velocity must be positive.
3. The force with which an object is thrown will not effect the acceleration in the y-direction. 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. If an object is thrown down at 100 km/hr, it will be accelerating as fast as an object that was only dropped, because while acceleration affects velocity, velocity does not affect gravitational acceleration.
