Review(1-D): For constant acceleration we found X=Xo +vot 0+ at a= const a few other useful formulas V。+V a(x Physics 121: Lecture 6, Pg 6
Physics 121: Lecture 6, Pg 6 Review (1-D): For constant acceleration we found: x a v t t t v = v + at 0 2 0 0 2 1 x = x + v t + at a = const A few other useful formulas : v v 2a(x x ) (v v) 2 1 v 0 2 0 2 av 0 − = − = + vav
2-D Kinematics For 2-D, we simply apply the 1-D equations to each of the component equations △1 y=yr-yi △t △t Which can be combined into the vector equations Physics 121: Lecture 6, Pg 7
Physics 121: Lecture 6, Pg 7 2-D Kinematics For 2-D, we simply apply the 1-D equations to each of the component equations. t v a x x = t x vx = t y vy = t v a y y = f i x = x − x f i y = y − y Which can be combined into the vector equations:
2-D Kinematics So for constant acceleration we get a= const 0 +a t +vt+1 a t2 (where a, V, Vo, r, ro, are all vectors) Physics 121: Lecture 6, Pg 8
Physics 121: Lecture 6, Pg 8 2-D Kinematics So for constant acceleration we get: a = const v = v0 + a t r = r0 + v0 t + 1 /2 a t 2 (where a, v, v0 , r, r0 , are all vectors)
3-D Kinematics Most 3-D problems can be reduced to 2-D problems when acceleration is constant Choose y axis to be along direction of acceleration Choose x axis to be along the other direction of motion Example: Throwing a baseball (neglecting air resistance) Acceleration is constant(gravity) Choose y axis up: ay=-9 Choose x axis along the ground in the direction of the throw Physics 121: Lecture 6, Pg 9
Physics 121: Lecture 6, Pg 9 3-D Kinematics Most 3-D problems can be reduced to 2-D problems when acceleration is constant; Choose y axis to be along direction of acceleration. Choose x axis to be along the “other” direction of motion. Example: Throwing a baseball (neglecting air resistance). Acceleration is constant (gravity). Choose y axis up: ay = -g. Choose x axis along the ground in the direction of the throw
“xand“y" components of motion are independent A man on a train tosses a ball straight up in the air View this from two reference frames Reference frame y motion: a=-gy on the moving train X motion: X= Vot Reference frame on the ground Physics 121: Lecture 6, Pg 10
Physics 121: Lecture 6, Pg 10 “x” and “y” components of motion are independent. A man on a train tosses a ball straight up in the air. View this from two reference frames: Reference frame on the ground. Reference frame on the moving train. y motion: a = -g y x motion: x = v0 t