Phys205A_Lecture24

Physics for Scientists & Engineers with Modern Physics (4th Edition)

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Chapter 9 Center of mass
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The Center of Mass z There is a special point in a system or object, called the center of mass , that moves as if all of the mass of the system is concentrated at that point z The system will move as if an external force were applied to a single particle of mass M located at the center of mass z M is the total mass of the system
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Center of Mass, Coordinates z The coordinates of the center of mass are z M is the total mass of the system z Use the active figure to observe effect of different masses and positions CM ii i i i mx x M my y M mz z M = = =
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Center of Mass, position z The center of mass in three dimensions can be located by its position vector, z For a system of particles, z is the position of the i th particle, defined by ˆˆˆ ii i i xyz =++ rijk CM r r 1 CM i i i m M = rr i r r
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Center of Mass, Extended Object z Similar analysis can be done for an extended object z Consider the extended object as a system containing a large number of particles z Since particle separation is very small, it can be considered to have a constant mass distribution CM 1 dm M = rr For an extended object,
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Center of Mass, Symmetric Object z The center of mass of any symmetric object lies on an axis of symmetry and on any plane of symmetry z If the object has uniform density
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Center of Gravity z Each small mass element of an extended object is acted upon by the gravitational force z The net effect of all these forces is equivalent to the effect of a single force acting through a point called the center of gravity z If is constant over the mass distribution, the center of gravity coincides with the center of mass M g r g r
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Finding Center of Mass, Irregularly Shaped Object z Suspend the object from one point z The suspend from another point z The intersection of the resulting lines is the center of mass
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Phys205A_Lecture24 - Chapter 9 Center of mass The Center of...

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