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l8anno - The Formula rOP(t = rOP s(t v P = | v P | et 2 |...

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“The Formula” 2 | | | | | | ( ) ( ( )) OP OP P P P t P P t n d t s t dt ρ + = = = v v e v a v 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.
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 fixed stars . 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 1 1 2 2 3 3 1 3 2 2 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ( ) ( ) ( ) ( ) ( ) ) i i i i i m t t m t t m t t t m t m t m t t t t m t t t t t t t = + = + = + + + = + + + + + = a F f f a F f f a F f f a a a F F F a F System of particles When summed the internal forces cancel ij ji = f f
Mass Center 1 1 2 2 3 1 2 3 3 Total mass OC i i i i i i i m m m m m m m m m m + + = + + = = R R 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

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