Physics 121, Sections 9, 10, 11, and 12 Lecture 6 Today's Topics Homework 2: Due Friday Sept 16@6: 00PM Ch3:#2,11,18,20,25,32,36,46,50,and56 Chapter 4: Motion in 2-D Review of vectors Projectile motion Relative velocity More examples of FBD's Physics 121: Lecture 6, Pg 1
Physics 121: Lecture 6, Pg 1 Physics 121, Sections 9, 10, 11, and 12 Lecture 6 Today’s Topics: Homework 2: Due Friday Sept. 16 @ 6:00PM Ch.3: # 2, 11, 18, 20, 25, 32, 36, 46, 50, and 56. Chapter 4: Motion in 2-D Review of vectors Projectile motion Relative velocity More examples of FBD’s
Katzenstein Distinguished Lecture Prof franck Wilczek Nobel Prize in physics 2004 From mit Title: The Universe is a Strange Place Where: Room P-36 When: Friday at 4: 00PM Refreshments at 3: 00 PM in front of P-36 Come for a great talk Physics 121: Lecture 6, Pg 2
Physics 121: Lecture 6, Pg 2 Katzenstein Distinguished Lecture Prof. Franck Wilczek Nobel Prize in Physics 2004 From MIT Title: The Universe is a Strange Place Where: Room P-36 When: Friday at 4:00PM Refreshments at 3:00 PM in front of P-36 Come for a great talk
Unit Vectors. A Unit Vector is a vector having length and no units U It is used to specify a direction Unit vector u points in the direction of U. G Often denoted with a hat.u=d Useful examples are the cartesian unit vectors[i,,kI point in the direction of the X, y and z axes R=+rj+「k k Physics 121: Lecture 6, Pg 3
Physics 121: Lecture 6, Pg 3 Unit Vectors: A Unit Vector is a vector having length 1 and no units. It is used to specify a direction. Unit vector u points in the direction of U. Often denoted with a “hat”: u = û U û x y z i j k Useful examples are the cartesian unit vectors [ i, j, k ] point in the direction of the x, y and z axes. R = rx i + ry j + rzk
Vector addition using components: Consider C =A +B (a)C=(Axi+Avi)+(Bxi+ Bj)=(Ax+ Bx)i+(A+ Bv)i (b)C=(Cxi+ Cy) Comparing components of (a) and(b) C=A+B、 B C=A +B B A Physics 121: Lecture 6, Pg 4
Physics 121: Lecture 6, Pg 4 Vector addition using components: Consider C = A + B. (a) C = (Ax i + Ay j ) + (Bx i + By j ) = (Ax + Bx )i + (Ay + By )j (b) C = (Cx i + Cy j ) Comparing components of (a) and (b): Cx = Ax + Bx Cy = Ay + By C A Bx By B Ax Ay
Lecture 6 ACT 1 Vector Addition Vector A=(0, 2] Vector B= 3,01 VectorC=(1, -4 What is the resultant vector. D. from adding A+B+C? (a)3,-4 (b){,-2} (C)5-2} Physics 121: Lecture 6, Pg 5
Physics 121: Lecture 6, Pg 5 Lecture 6, ACT 1 Vector Addition Vector A = {0,2} Vector B = {3,0} Vector C = {1,-4} What is the resultant vector, D, from adding A+B+C? (a) {3,-4} (b) {4,-2} (c) {5,-2}
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
