A Particle in Motion
A Particle in Motion
Agenda today 1.The relationship between velocity,acceleration and displacement 2.Projectile motion 3.Circular movement 4.Relative movement
Agenda today 1. The relationship between velocity, acceleration and displacement 2. Projectile motion 3. Circular movement 4. Relative movement
Ockham's razor and modeling Particle(质点) A point with no shape and size ,but has mass Translational movement(平动) Each point of the body has the same trail in the motion Reference Frames(参照系)
Particle（质点） Reference Frames（参照系） Translational movement（平动） Ockham’s razor and modeling A point with no shape and size ,but has mass Each point of the body has the same trail in the motion
"I am thinking therefore I exist." (Latin:Cogito ergo sum) from the Discourse on Method Coordinate System: （坐标系) Cartesian coordinate system(直角坐标系) polar system(极坐标系)
Coordinate System：（坐标系） Cartesian coordinate system（直角坐标系） polar system（极坐标系） "I am thinking therefore I exist." (Latin: Cogito ergo sum) from the Discourse on Method
Position and Displacement Vector( 置矢量和位移矢量) F=xi+y月+z水 P(xy,z） r=vx2+y2+22 ewsn-eosB=}cosy-=月
Position and Displacement Vector(位 置矢量 和位移矢量 ） P(x,y,z) r z y x o r xi yj zk 2 2 2 r x y z r z r y r X cos cos cos
F=r(⑦ In Cartesian coordinate system F =x(t)i +y(t)j+z(t)k In component form x =x(t) y=y() z=z(t)
r x t i y t j z t k ( ) ( ) ( ) r r(t) In Cartesian coordinate system In component form ( ) ( ) ( ) z z t y y t x x t x o z y r
△7=fB-F4=AB △F=△xi+△y+△xk Displacement Vector △=V△x2+△y2+2
r rB rA AB r xi yj zk 2 2 2 r x y z Displacement Vector
Velocity and Speed Velocity describe the rate of change of the position of the particle on its trajectory. Average Velocity:(平均速度) △F
Velocity and Speed Velocity describe the rate of change of the position of the particle on its trajectory. Average Velocity:（平均速度） m s t r v B A o z y x A r B r r
Instantaneous Velocity(瞬时速度)： 立=lim △F dr (ms） △t-→0 v=vi +V,j+vk dx dz dt b= d dt
v==V++图 Speed(速率) Average speed(平均速率) = △S ms） △t Instantaneous speed(即时速率) ds lim △t→0
2 2 2 x y z v v v v v Speed（速率） 1 m s t s v Average speed（平均速率） Instantaneous speed（即时速率） dt ds t s v t lim 0 s r B A