Chapter 9a - Chapter 9 Center of Mass and Linear Momentum...

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Chapter 9 Center of Mass and Linear Momentum (part 1)
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The point mass The point mass is a physical approximation of a real object that has dimensions. How good is this this approximation??? Can we apply Newton’s laws and all we learned so far to a big, extended object, or to a system of objects that are not even attached to each other?
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System of particles A body can have a complicated shape We can represent the body as a sum of smaller parts Apply Newton’s law to each part. r F i = m i r a i = m i d 2 r r i dt 2 r F = r F i i = 1 n = m i d 2 r r i dt 2 = i = 1 n d 2 m i r r i dt 2 = d 2 dt 2 m i r r i i = 1 n i = 1 n r F = M d 2 dt 2 1 M m i r r i i = 1 n r F = M r a = M d 2 r r com dt 2 r r com = 1 M m i r r i i = 1 n M = m i i = 1 n m i , r r i r F i , r a i
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The center of mass ( COM ) of a system of particles is the point that moves as though the system’s mass is concentrated in this point and all external forces are applied there. Important note: We can substitute the entire system with a single point! COM is a geometrical point (it might be outside of the
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Chapter 9a - Chapter 9 Center of Mass and Linear Momentum...

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