Chapter 4 Motion in tyo and three
Chapter 4 Motion in two and three dimensions
TWo principles for 2D and 3D motions 1)The principle of independence of force 2)The principle of superposition of motion F F3 F2
Two principles for 2D and 3D motions: 1) The principle of independence of force 2) The principle of superposition of motion F1 F2 F3
Scio4小 oijoririhree c9so5 wiin constant accelerator Now we consider a particle move in three dimensions with constant acceleration. We can represent the acceleration as a vector a=a ita i+ak The particle starts at t=0 with initial position -xo i+ yo j+=ok and an initial velocity vo=vo, i+vov j+vo k
The particle starts at t=0 with initial position and an initial velocity . Section 4-1 Motion in three dimensions with constant acceleration Now we consider a particle move in three dimensions with constant acceleration. We can represent the acceleration as a vector: → a = a i+ a j+ a k x y z → r = x i+ y j+ z k 0 0 0 o → v = v i+ v j+ v k 0 0x 0 y 0z
a,a constant L ar, a,a, all constants Vx vox to t +a t v=v+at(4-1) +ot In a similar way x=Xo+ vo.t y=Vo+volta,t r=r+vot+ at 2=z0+v=2+a2t (4-2)
In a similar way: v v a t x x x = + 0 v v a t y y y = + 0 v v a t z z z = + 0 v v a t → → → = 0 + a, a constant → , , , x y z a a a all constants x v x ax t x t 2 0 0 2 1 = + + z v z az t z t 2 0 0 2 1 = + + y v y ay t y t 2 0 0 2 1 = + + 2 0 0 2 1 r r v t a t → → → → = + + （4-1） （4-2）
co42小yon3 s lays intree clmersjona yector」for∫」 ∑ F=ma(43) Which includes the three component equations ∑∑∑ F=max F=mas F=ma,(4-4)
Section 4-2 Newton’s laws in three dimensional vector form (4-3) Which includes the three component equations (4-4) → → F = ma Fx = max Fy = may Fz = maz