l8anno - The Formula rOP (t ) = rOP ( s (t ) v P = | v P |...

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“The Formula” 2 || () (() ) OP OP P P Pt P n d ts t dt ρ + = = = vv e v av e r e r
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Newton ` s Laws (1687) 1) A particle acted upon by a zero resultant force moves at constant velocity 2) F is proportional to the time derivative of the particle ` s momentum m v ( m is mass and v is velocity) 3) The interaction of two particles is through a pair of self equilibrating forces.
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Notes: depends on the reference frame. Newton ` s laws apply to inertial frames. Such frames may translate, (but not rotate) with constant velocity provided is not too large (speed of light) relative to the l fixed stars z . m must not be too small (sub atomic) Particles have constant mass so v F || v F F P v /F m v = m & v = m a
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2 F 2 m 21 f 12 f 1 m 1 F 2 a 1 a 3 m 31 f 13 f 3 a 3 F 32 f 23 f 1 1 1 12 13 2 2 21 23 3 3 3 31 32 11 2 2 3 3 1 3 2 2 () ( ) ii i mt t t t t m t m t t t t m t t t t t t t =+ ++= + + + + + = ∑∑ aF f f f f f f aaa F F F System of particles When summed the internal forces cancel ij ji = ff
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Mass Center 11 2 2 3 123 3 Total mass OC ii i i i i i mm m m m m ++ = = = RR R r R 2 m 1 m 3 m O 1 e 2 e 3 R 1 R 2 R OC r C
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m i a i ( t ) i ! = F i ( t ) i ! m i && R i ( t ) i ! = F i ( t ) i ! m i R i ( t ) i ! •• = F i ( t ) i ! m i i ! m i R i ( t ) i ! m i i ! " # $
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This note was uploaded on 01/26/2012 for the course TAM 212 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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l8anno - The Formula rOP (t ) = rOP ( s (t ) v P = | v P |...

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