course-summary1 - Summary on unit 1 (update: 10/31/09) Sec...

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Summary on unit 1 (update: 10/31/09) Sec 1.1-1.9. Coord-vector: r = < x;y;z > = r ^ r , r = p x 2 + y 2 + z 2 ; ^ r = < cos± x ;cos± y ;cos± z > . For 2D case, r = p x 2 + y 2 + z 2 ,^ r = < cos±;sin± > . Displacement: ± r = r f ± r i Velocity: De²nition of average velocity- v av = ± r = ± t . ² Position up date : r f = r i + v av ± t . ² Instantaneous velocity: v = Lim ± t ! 0 r = ± t ) . Instantaneous acceleration: a = d v =dt . ² If acceleration a = d v =dt = F =m is const., v av = ( v f + v i ) = 2. If not const. set v av ³ v f . Momentum: p = ²m v , ² = 1 = p 1 ± ³ 2 , ³ = j v j =c . ² Nonrelativistic approximation(NR): ² ! 1, p = m v . ² Identity: ³ = ³²= p 1 + ( ³² ) 2 , where ³² = p=cm . The extended Newton’s law of motion: F = ± p = ± t . ² If F = 0 ; p = p ^ p = constant . This is Newton’s ²rst law. ² In NR case, it leads to F = ± p = ± t =m a . This is Newton’s second law, with de²nition a = d v =dt . ² For 1-d, a=const. Mom-P: v f = v i + a ± t , pos-update s = ( v i + v f t = v i ± t + (1 = 2) a ± t 2 . ² If F 6 = 0, multiplying both sides by ± t , it states that it is the impact of the impulse, F ± t
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