Center of gravity lab rod4/18/2023 ![]() 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. In the second example (the salt crystal), notice that there is no mass at all at the location of the center of mass.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 Earth-moon system example, this means including the mass of Earth. However, you must still include the mass of the object at your origin in your calculation of M, the total mass Equation 9.19. That choice automatically defines its distance in Equation 9.29 to be zero. ![]() For center-of-mass calculations, it often makes sense to choose your origin to be located at one of the masses of your system. As with all problems, you must define your coordinate system and origin.Two crucial concepts come out of these examples: Is the center of mass of this crystal necessarily at the geometric center of the crystal? It is made up of a huge number of unit cells. Suppose you have a macroscopic salt crystal (that is, a crystal that is large enough to be visible with your unaided eye). Therefore, there is no meaningful application of the center of mass of a unit cell beyond as an exercise. SignificanceAlthough this is a great exercise to determine the center of mass given a Chloride ion at the origin, in fact the origin could be chosen at any location. Similar calculations give r CM, y = r CM, z = 1.18 × 10 −10 m r CM, y = r CM, z = 1.18 × 10 −10 m (you could argue that this must be true, by symmetry, but it’s a good idea to check). We want to be able to handle this, as well. This implies that the constituent particles are applying internal forces on each other, in addition to the external force that is acting on the object as a whole. Then too, an extended object might change shape as it moves, such as a water balloon or a cat falling ( Figure 9.26). How do we include these facts into our calculations? There are many different types of particles, and they are generally not distributed uniformly in the object. ![]() ![]() A car has an engine, steering wheel, seats, passengers a football is leather and rubber surrounding air a brick is made of atoms. We have been avoiding an important issue up to now: When we say that an object moves (more correctly, accelerates) in a way that obeys Newton’s second law, we have been ignoring the fact that all objects are actually made of many constituent particles.
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