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24-center of mass - Phys 211 Systems of Particles Center of...

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Phys 211 3/23/09 Systems of Particles Center of Mass
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Center of Mass Complete the following statement: The center of mass is a) the region of an object where the density has the largest value. b) the region of an object where most of the mass is located. c) the point within an object that moves as if all of the object’s mass where located there. d) the point at the geometrical center of an object. e) the only point on an object at which the gravitational force acts.
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Center of Mass Center of Mass - (CM, COM) - Point that moves as though (1) all of the system’s mass were concentrated there (2) all external forces were applied there
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CM Determination x cm = m 1 x 1 + m 2 x 2 m 1 + m 2 If m 1 =m 2 , CM halfway between x cm = mx 1 + mx 2 2 m = 1 2 ( x 1 + x 2 ) = x 1 + 1 2 ( x 2 x 1 ) x cm = m 1 x 1 + m 2 x 2 + ... + m n x n m 1 + m 2 + ... + m n = m i x i i m i i = m i x i i M In general Works in x,y,z direction independently!
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Sun, Earth, Mars Consider the Earth and Mars in their orbit around the Sun.
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