Similar calculations give
(you could argue that this must be true, by symmetry, but it’s a good idea to check).
Significance
As it turns out, it was not really necessary to convert the mass from atomic mass units (u) to kilograms, since the units divide out when calculating
anyway.
To express
in terms of magnitude and direction, first apply the three-dimensional Pythagorean theorem to the vector components:
Since this is a three-dimensional problem, it takes two angles to specify the direction of
. Let
be the angle in the
x ,
y -plane, measured from the +
x -axis, counterclockwise as viewed from above; then:
Let
be the angle in the
y ,
z -plane, measured downward from the +
z -axis; this is (not surprisingly):
Thus, the center of mass is at the geometric center of the unit cell. Again, you could argue this on the basis of symmetry.
Check Your Understanding Suppose you have a macroscopic salt crystal (that is, a crystal that is large enough to be visible with your unaided eye). It is made up of a
huge number of unit cells. Is the center of mass of this crystal necessarily at the geometric center of the crystal?
On a macroscopic scale, the size of a unit cell is negligible and the crystal mass may be considered to be distributed homogeneously throughout the crystal. Thus,
where we sum over the number
N of unit cells in the crystal and
m is the mass of a unit cell. Because
Nm =
M , we can write
This is the definition of the geometric center of the crystal, so the center of mass is at the same point as the geometric center.
As with all problems, you must define your coordinate system and origin. For center-of-mass calculations, it often makes sense to choose your origin to be located at one of the masses of your system. That choice automatically defines its distance in
[link] to be zero. However, you must still include the mass of the object at your origin in your calculation of
M , the total mass
[link] . In the Earth-moon system example, this means including the mass of Earth. If you hadn’t, you’d have ended up with the center of mass of the system being at the center of the moon, which is clearly wrong.
In the second example (the salt crystal), notice that there is no mass at all at the location of the center of mass. This is an example of what we stated above, that there does not have to be any actual mass at the center of mass of an object.
Questions & Answers
I'm interested in biological psychology and cognitive psychology
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
