Chapter 3: Kinematics in Two Dimensions
|
|
- Merry King
- 6 years ago
- Views:
Transcription
1 Chapter 3: Kinematics in Two Dimensions Vectors and Scalars A scalar is a number with units. It can be positive, negative, or zero. Time: 100 s Distance and speed are scalars, although they cannot be negative because of the way they are defined. A vector is a quantity which specifies magnitude and direction. Velocity:4 m/s East Acceleration: 10 m/s to the right
2 Notation Vector quantities are represented using bold type or an arrow above the symbol. The magnitude of a vector (a scalar) is represented using the absolute value symbol or without bold type: velocity: v = v = 5 m/s East v = v =5m/s
3 Arrow Representation Arrows are also used to represent vectors themselves. The length of the arrow is proportional to the magnitude. The direction of the arrow indicates the direction of the vector. 4 m/s East m/s North
4 Adding Vectors Only add vectors with the same units. For example: v 3 = v 1 + v is OK, but v 3 = x 1 + v does not make sense Remember that a vector -AA points opposite to A. A A
5 Adding Vectors Graphically To add two vectors A + B, put the tail of B at the tip of faa and connect the tail of faa to the tip of B. Use a ruler and protractor to determine the magnitude and direction of C.
6 Subtracting Vectors, and Multiplication by a Scalar The negative of a vector is a vector having the same length, but pointing in the opposite direction So we can define the subtraction of one vector from another as A vector can also be multiplied by a scalar c. We define this product so that cv has the same direction as V and a magnitude c V.
7 Components of a Vector A vector can be specified either by its magnitude and direction, or by its components in a coordinate system. r,θθ r x,r y
8 Be Careful The components of a vector are not always positive. The angle is not always defined relative to the x axis.
9 Trigonometric Functions SOH CAH TOA opposite side sinθ = = hypotnuse cosθ = tanθ = A A x + A y adjacent side = hypotnuse opposite side = adjacent side A y A A Ax A A A y x = A + A A x θ A A y Be careful with your calculator! Are you using degrees or radians?
10 Example Find the x and y components of a vector of magnitude 5, if its angle relative to the x axis is 00. ( ) A = Acosθ = 5cos 00 = 4.70 x ( ) A = Asinθ = 5sin 00 = 1.71 y
11 Adding Vectors Using Components Break vectors up into components. Add components. Find magnitude and direction of the sum from its components.
12 Example 1. The vectors are shown in the figure below. Their magnitudes are given are given in arbitrary units. Determine the sum of the three vectors. Give the resultant in terms of (a) components, (b) magnitude and angle with x axis.
13 Unit Vectors A unit vector is a vector with magnitude equal to 1 and pointing in a certain defined direction. Example: the unit vector in the x direction is usually written: ˆ xˆ or i Now I can write a vector as its components multiplied by the unit vector: A= A xˆ+ A yˆ x or A= Aiˆ+ A ˆj where A x and A y are scalars. x y j y
14 Example Write the vector in the figure in unit vector notation. y θ v v = 10 x θ = 50
15 Position and Displacement Vectors The position vector r points from the origin to a particular location. The displacement vector Δr indicates the change in position: Δr = r f - r i
16 Writing of displacement in terms of components and unit vectors, Δ r = ( x x ) iˆ+ ( y y ) ˆj+ ( z z ) kˆ We defined the instantaneous velocity as v = = Δt Δr dr lim Δ t 0 So we can write the instantaneous velocity as, dx ˆ dy ˆ dz v = i j kˆ v ˆ ˆ ˆ xi vy j vk z dt + dt + dt = + + dt
17 Likewise for acceleration, Δv aav = = Δ t v v Δ t 1 The instantaneous acceleration is given by so a lim v Δ = = dv Δ t 0 Δ t dt dv dv x ˆ y ˆ dvz a = i j kˆ a ˆ ˆ ˆ xi ay j azk + + = + + dt dt dt
18 Acceleration occurs whenever there is a change in velocity. If a car travels in a circle at a constant speed of 50 mi/hr, is it accelerating? YES! Because the direction of the velocity vector is changing.
19 Kinematic Equations for Constant Acceleration in Dimensions x-component y-component 1 x = xo + vxo t + ax t v = v + a t x xo x vx vxo ax x xo y = y + v t+ a t 1 o yo y v = v + a t y yo y = + ( ) v = v + a ( y y ) y yo y o
20 Projectile Motion Motion in the x direction is independent from motion in the y direction. We use the same equations from Chapter, but for each dimension separately. There are not really any new equations in this chapter.
21 The equations you need. 1 x x= x0 + v0xt+ a t 1 y = y0 + v0yt+ ayt NOTE v = v + a t x 0x x v = v + a t y 0 y y ( ) v = v + a x x x 0x + x f i ( ) v = v + a y y y 0 y y f i For projectile motion problems, a x (the horizontal componant of the acceleration) will usually be zero since usually there will be no acceleration in the x direction
22 Projectile Motion Assume that acceleration of gravity is constant, downward and has a magnitude of g = 9.81 m/s Air resistance is ignored The Earth s rotation is ignored Horizontal velocity is constant: because a x = 0 Vertical motion governed by the constant acceleration of gravity
23 Motion of a Projectile Launched Horizontally The dots represents the position of the object every 0.05 s. y 0 = 8 m; x 0 = 0 v 0y = 0; v 0x = 6 m/s a y = m/s ; a x = 0 t = 1 s 1. Verify the position of the object at t = 1s.. What would be the position of the object at t = 1 s if it were dropped (v 0x = 0)?
24 1 x = 0 + v0x t y = y0 + v0yt + ayt x 1 = 6 1 = 6 m y = ( 1) = 3.1 m 1 ( ) y = = 3.1 m x = 0
25 Example Pitcher s mounds are raised to compensate for the vertical drop of the ball as it travels 18 m to the catcher. (a) If a pitch is thrown horizontally with an initial speed of 3 m/s (71 mi/hr), how far does it drop by the time it reaches the catcher? (b) If the speed of the pitch is increased, does the drop distance increase, decrease or stay the same? Explain. (c) If this baseball game were to be played on the moon, would (c) If this baseball game were to be played on the moon, would the drop distance increase, decrease, or stay the same? Explain.
26 ( a) x= v t 0x 18 = 3t t = 0.56 s reach catcher reach catcher 1 1 y = y ( ) 0 + v0yt 9.8t y y0 = = 1.54 m y0 y = m (b) If the speed of the pitch increases, the time gets smaller, so the drop distance is less (c) On the moon g is less than 9.8 m/s, so the drop distance is less.
27 General Launch Angle Consider an object launched from the origin at an angle θ with respect to the horizontal. y v o θ x What are the x and y components of the initial velocity vector?
28 Example: On a hot summer day a young girl swings on a rope above the local swimming hole. When she lets go of the rope her initial velocity is.55 m/s at an angle of 35.0 above the horizontal. If she is in flight for 1.60 s, how high above the water was she when she let go of the rope? What is the girl s minimum speed during her flight? What is her acceleration at the top of her trajectory?
29 1 y = y0 + v0sinθt 9.81t 1 0 = y0 +.5sin 35 t 9.81t 1 0 = y0 +.5sin y 0 = m ( ) ( ) Girl s minimum speed is at the maximum in her trajectory! Can you see why? Girl s acceleration is 9 81 m/s at the top of her trajectory Girl s acceleration is 9.81 m/s at the top of her trajectory. What is her acceleration at other points on her trajectory?
30 Range The range R of a projectile is the horizontal distance it travels before landing. R v = 0 sin θ g (BE CAREFUL!, This equation only works when the initial and final elevation are the same) You should try to derive this equation! It s not difficult. Just remember that x=r when the projectile hits the ground. What angle θ results in the maximum range? Remember 0 θ 90. What if we do not ignore air resistance?
31 Example A projectile is fired at 00 m/s at an angle of 45 degrees above the horizontal. How far does it travel? R v = 0 sin θ g (00m/s) R o = sin((45 )) = 98m/s 9.8m/s 4081m
32 Maximum Height The maximum height (and therefore the hang time )ofa projectile depends only on the vertical component of its initial velocity. At y max, the vertical velocity v y is zero. v 0 y y = = v max v 0 0 y sin v = + aδy 0 θ + ( g) y sin θ g max
33 Example From the previous example, how high does the projectile go? y v = o max sin θ g ( 00m / s) o (45 ) y max = = sin (9.8) 100m
34 Uniform Circular Motion Consider a particle moving in a circle. v 1 Is the particle accelerating? lim v Δ a = = dv Δ t 0 Δ t dt - The speed of the particle is constant - The direction of the ball is changing v
35 What is the direction of the acceleration?
36 Magnitude of Radial Acceleration This type acceleration is called centripetal or radial acceleration. The magnitude of the acceleration is given by, a R = v r
37 Period and Frequency The amount of time that it takes the particle to make one full revolution is called the period, T. The number of times that the particle goes around the circle per unit time is called the frequency, y,f. T 1 = f The speed of a particle moving around in a circle is given by, distance π r v= = = π rf time T
38 Example 33 A h t tt th th th h t( 73k ) ith 33. A shotputter throws throws the shot (mass = 7.3 kg) with an initial speed of 14.0 m/s at a 40 angle to the horizontal. Calculate the horizontal distance traveled by the shot if it leaves the athlete s hand at a height of. m above the ground.
39 Example 18. The position of a particular particle as a function of time is given by, ˆ ˆ r = (7.60 ti j t k ˆ ) m (a) Determine the particle s velocity and acceleration as a function of time. (b) Describe the motion in each direction.
40 Example Chapter #40. A space vehicle accelerates uniformly from 65 m/s at t=0 to 16 m/s at 10.0 s. How far did it move bt between t=.0s 0 and dt= s?
41 Example A baseball is hit at an angle of 50 relative to the horizontal with an initial speed of 10 miles/hour. ()H hi hd it? (a) How high does it go? (b) How long does it spend in the air? (c) How far does it travel?
Chapter 4. Motion in Two Dimensions. Professor Wa el Salah
Chapter 4 Motion in Two Dimensions Kinematics in Two Dimensions Will study the vector nature of position, velocity and acceleration in greater detail. Will treat projectile motion and uniform circular
More informationChapter 3. Kinematics in Two Dimensions
Chapter 3 Kinematics in Two Dimensions 3.1 Trigonometry 3.1 Trigonometry sin! = h o h cos! = h a h tan! = h o h a 3.1 Trigonometry tan! = h o h a tan50! = h o 67.2m h o = tan50! ( 67.2m) = 80.0m 3.1 Trigonometry!
More informationAdding Vectors in Two Dimensions
Slide 37 / 125 Adding Vectors in Two Dimensions Return to Table of Contents Last year, we learned how to add vectors along a single axis. The example we used was for adding two displacements. Slide 38
More information3 Vectors and Two- Dimensional Motion
May 25, 1998 3 Vectors and Two- Dimensional Motion Kinematics of a Particle Moving in a Plane Motion in two dimensions is easily comprehended if one thinks of the motion as being made up of two independent
More informationChapter 4. Motion in Two Dimensions
Chapter 4 Motion in Two Dimensions Kinematics in Two Dimensions Will study the vector nature of position, velocity and acceleration in greater detail Will treat projectile motion and uniform circular motion
More informationVectors and 2D Kinematics. AIT AP Physics C
Vectors and 2D Kinematics Coordinate Systems Used to describe the position of a point in space Coordinate system consists of a fixed reference point called the origin specific axes with scales and labels
More informationCHAPTER 3 KINEMATICS IN TWO DIMENSIONS; VECTORS
CHAPTER 3 KINEMATICS IN TWO DIMENSIONS; VECTORS OBJECTIVES After studying the material of this chapter, the student should be able to: represent the magnitude and direction of a vector using a protractor
More informationProgressive Science Initiative. Click to go to website:
Slide 1 / 246 New Jersey Center for Teaching and Learning Progressive Science Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students and
More informationCHAPTER 3 MOTION IN TWO AND THREE DIMENSIONS
CHAPTER 3 MOTION IN TWO AND THREE DIMENSIONS General properties of vectors displacement vector position and velocity vectors acceleration vector equations of motion in 2- and 3-dimensions Projectile motion
More informationDemo: x-t, v-t and a-t of a falling basket ball.
Demo: x-t, v-t and a-t of a falling basket ball. I-clicker question 3-1: A particle moves with the position-versus-time graph shown. Which graph best illustrates the velocity of the particle as a function
More informationDescribing motion: Kinematics in two dimension
Describing motion: Kinematics in two dimension Scientist Galileo Galilei Issac Newton Vocabulary Vector scalars Resultant Displacement Components Resolving vectors Unit vector into its components Average
More information3.2 Projectile Motion
Motion in 2-D: Last class we were analyzing the distance in two-dimensional motion and revisited the concept of vectors, and unit-vector notation. We had our receiver run up the field then slant Northwest.
More informationIn this activity, we explore the application of differential equations to the real world as applied to projectile motion.
Applications of Calculus: Projectile Motion ID: XXXX Name Class In this activity, we explore the application of differential equations to the real world as applied to projectile motion. Open the file CalcActXX_Projectile_Motion_EN.tns
More informationMotion in Two or Three Dimensions
Chapter 3 Motion in Two or Three Dimensions PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 3 To use vectors
More informationChapter 4. Motion in Two Dimensions. With modifications by Pinkney
Chapter 4 Motion in Two Dimensions With modifications by Pinkney Kinematics in Two Dimensions covers: the vector nature of position, velocity and acceleration in greater detail projectile motion a special
More information( ) ( ) A i ˆj. What is the unit vector  that points in the direction of A? 1) The vector A is given by = ( 6.0m ) ˆ ( 8.0m ) Solution A D) 6 E) 6
A i ˆj. What is the unit vector  that points in the direction of A? 1) The vector A is given b ( 6.m ) ˆ ( 8.m ) A ˆ i ˆ ˆ j A ˆ i ˆ ˆ j C) A ˆ ( 1 ) ( i ˆ ˆ j) D) Aˆ.6 iˆ+.8 ˆj E) Aˆ.6 iˆ.8 ˆj A) (.6m
More information2. Two Dimensional Kinematics
. Two Dimensional Kinematics A) Overview We will begin by introducing the concept of vectors that will allow us to generalize what we learned last time in one dimension to two and three dimensions. In
More informationChapter 2. Kinematics in One Dimension. continued
Chapter 2 Kinematics in One Dimension continued 2.6 Freely Falling Bodies Example 10 A Falling Stone A stone is dropped from the top of a tall building. After 3.00s of free fall, what is the displacement
More informationChapter 4. Motion in Two Dimensions
Chapter 4 Motion in Two Dimensions Kinematics in Two Dimensions Will study the vector nature of position, velocity and acceleration in greater detail Will treat projectile motion and uniform circular motion
More informationQuiz No. 1: Tuesday Jan. 31. Assignment No. 2, due Thursday Feb 2: Problems 8.4, 8.13, 3.10, 3.28 Conceptual questions: 8.1, 3.6, 3.12, 3.
Quiz No. 1: Tuesday Jan. 31 Assignment No. 2, due Thursday Feb 2: Problems 8.4, 8.13, 3.10, 3.28 Conceptual questions: 8.1, 3.6, 3.12, 3.20 Chapter 3 Vectors and Two-Dimensional Kinematics Properties of
More informationChapter 3 Kinematics in Two Dimensions; Vectors
Chapter 3 Kinematics in Two Dimensions; Vectors Vectors and Scalars Addition of Vectors Graphical Methods (One and Two- Dimension) Multiplication of a Vector by a Scalar Subtraction of Vectors Graphical
More informationSTUDENT NAME: STUDENT id #: NOTE: Clearly write out solutions and answers (circle the answers) by section for each part (a., b., c., etc.
GENERAL PHYSICS PH 1-3A (Dr. S. Mirov) Test 1 (09/17/07) Key STUDENT NAME: STUDENT id #: -------------------------------------------------------------------------------------------------------------------------------------------
More informationPHY 1114: Physics I. Quick Question 1. Quick Question 2. Quick Question 3. Quick Question 4. Lecture 5: Motion in 2D
PHY 1114: Physics I Lecture 5: Motion in D Fall 01 Kenny L. Tapp Quick Question 1 A child throws a ball vertically upward at the school playground. Which one of the following quantities is (are) equal
More informationCircular motion. Announcements:
Circular motion Announcements: Clicker scores through Wednesday are now posted on DL. Scoring is points for a wrong answer, 3 points for a right answer. 13 clicker questions so far, so max is 39 points.
More information2D and 3D Motion. with constant (uniform) acceleration
2D and 3D Motion with constant (uniform) acceleration 1 Dimension 2 or 3 Dimensions x x v : position : position : displacement r : displacement : velocity v : velocity a : acceleration a r : acceleration
More informationMotion in Two Dimensions. 1.The Position, Velocity, and Acceleration Vectors 2.Two-Dimensional Motion with Constant Acceleration 3.
Motion in Two Dimensions 1.The Position, Velocity, and Acceleration Vectors 2.Two-Dimensional Motion with Constant Acceleration 3.Projectile Motion The position of an object is described by its position
More informationVocabulary Preview. Oct 21 9:53 AM. Projectile Motion. An object shot through the air is called a projectile.
Projectile Trajectory Range Launch angle Vocabulary Preview Projectile Motion Projectile Motion An object shot through the air is called a projectile. A projectile can be a football, a bullet, or a drop
More informationChapter 4. Two-Dimensional Motion
Chapter 4. Two-Dimensional Motion 09/1/003 I. Intuitive (Understanding) Review Problems. 1. If a car (object, body, truck) moves with positive velocity and negative acceleration, it means that its a) speed
More informationKinematics in Two Dimensions; Vectors
Kinematics in Two Dimensions; Vectors Vectors & Scalars!! Scalars They are specified only by a number and units and have no direction associated with them, such as time, mass, and temperature.!! Vectors
More informationChapter 3: 2D Kinematics Tuesday January 20th
Chapter 3: 2D Kinematics Tuesday January 20th Chapter 3: Vectors Review: Properties of vectors Review: Unit vectors Position and displacement Velocity and acceleration vectors Relative motion Constant
More informationMotion in 2- and 3-dimensions. Examples: non-linear motion (circles, planetary orbits, etc.) flight of projectiles (shells, golf balls, etc.
Motion in 2- and 3-dimensions Examples: HPTER 3 MOTION IN TWO & THREE DIMENSIONS General properties of vectors the displacement vector position and velocity vectors acceleration vector equations of motion
More informationProjectile Motion. directions simultaneously. deal with is called projectile motion. ! An object may move in both the x and y
Projectile Motion! An object may move in both the x and y directions simultaneously! The form of two-dimensional motion we will deal with is called projectile motion Assumptions of Projectile Motion! The
More informationChapter 4. Motion in Two Dimensions
Chapter 4 Motion in Two Dimensions Kinematics in Two Dimensions Will study the vector nature of position, velocity and acceleration in greater detail Will treat projectile motion and uniform circular motion
More informationPhysics 201 Homework 1
Physics 201 Homework 1 Jan 9, 2013 1. (a) What is the magnitude of the average acceleration of a skier who, starting (a) 1.6 m/s 2 ; (b) 20 meters from rest, reaches a speed of 8.0 m/s when going down
More informationChapter 3. Vectors and Two-Dimensional Motion
Chapter 3 Vectors and Two-Dimensional Motion 1 Vector vs. Scalar Review All physical quantities encountered in this text will be either a scalar or a vector A vector quantity has both magnitude (size)
More informationObjectives and Essential Questions
VECTORS Objectives and Essential Questions Objectives Distinguish between basic trigonometric functions (SOH CAH TOA) Distinguish between vector and scalar quantities Add vectors using graphical and analytical
More informationChapter 4. Motion in Two Dimensions. Position and Displacement. General Motion Ideas. Motion in Two Dimensions
Motion in Two Dimensions Chapter 4 Motion in Two Dimensions Using + or signs is not always sufficient to fully describe motion in more than one dimension Vectors can be used to more fully describe motion
More informationNeed to have some new mathematical techniques to do this: however you may need to revise your basic trigonometry. Basic Trigonometry
Kinematics in Two Dimensions Kinematics in 2-dimensions. By the end of this you will 1. Remember your Trigonometry 2. Know how to handle vectors 3. be able to handle problems in 2-dimensions 4. understand
More informationPhysics 1-2 Mr. Chumbley
Physics 1-2 Mr. Chumbley Physical quantities can be categorized into one of two types of quantities A scalar is a physical quantity that has magnitude, but no direction A vector is a physical quantity
More informationWork and Energy (Work Done by a Constant Force)
Lecture 11 Chapter 7 Physics I 10.16.2013 Work and Energy (Work Done by a Constant Force) Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi Lecture Capture: http://echo360.uml.edu/danylov2013/physics1fall.html
More informationThe centripetal acceleration for a particle moving in a circle is a c = v 2 /r, where v is its speed and r is its instantaneous radius of rotation.
skiladæmi 1 Due: 11:59pm on Wednesday, September 9, 2015 You will receive no credit for items you complete after the assignment is due. Grading Policy Problem 3.04 The horizontal coordinates of a in a
More informationExample problem: Free Fall
Example problem: Free Fall A ball is thrown from the top of a building with an initial velocity of 20.0 m/s straight upward, at an initial height of 50.0 m above the ground. The ball just misses the edge
More informationChapter 3 Kinematics in Two Dimensions; Vectors
Chapter 3 Kinematics in Two Dimensions; Vectors Vectors and Scalars Units of Chapter 3 Addition of Vectors Graphical Methods Subtraction of Vectors, and Multiplication of a Vector by a Scalar Adding Vectors
More informationChapter 2 One-Dimensional Kinematics. Copyright 2010 Pearson Education, Inc.
Chapter 2 One-Dimensional Kinematics Units of Chapter 2 Position, Distance, and Displacement Average Speed and Velocity Instantaneous Velocity Acceleration Motion with Constant Acceleration Applications
More informationPhysics Chapter 3 Notes. Section 3-1: Introduction to Vectors (pages 80-83)
Physics Chapter 3 Notes Section 3-1: Introduction to Vectors (pages 80-83) We can use vectors to indicate both the magnitude of a quantity, and the direction. Vectors are often used in 2- dimensional problems.
More informationMOTION IN TWO OR THREE DIMENSIONS
MOTION IN TWO OR THREE DIMENSIONS 3 Sections Covered 3.1 : Position & velocity vectors 3.2 : The acceleration vector 3.3 : Projectile motion 3.4 : Motion in a circle 3.5 : Relative velocity 3.1 Position
More informationPhys101 First Major-111 Zero Version Monday, October 17, 2011 Page: 1
Monday, October 17, 011 Page: 1 Q1. 1 b The speed-time relation of a moving particle is given by: v = at +, where v is the speed, t t + c is the time and a, b, c are constants. The dimensional formulae
More informationKINEMATICS REVIEW VECTOR ALGEBRA - SUMMARY
1 KINEMATICS REVIEW VECTOR ALGEBRA - SUMMARY Magnitude A numerical value with appropriate units. Scalar is a quantity that is completely specified by magnitude. Vector requires both, magnitude and direction
More informationMath Review 1: Vectors
Math Review 1: Vectors Coordinate System Coordinate system: used to describe the position of a point in space and consists of 1. An origin as the reference point 2. A set of coordinate axes with scales
More informationChapter 3. Vectors and. Two-Dimensional Motion Vector vs. Scalar Review
Chapter 3 Vectors and Two-Dimensional Motion Vector vs. Scalar Review All physical quantities encountered in this text will be either a scalar or a vector A vector quantity has both magnitude (size) and
More informationPhysics 11 Chapter 3: Kinematics in Two Dimensions. Problem Solving
Physics 11 Chapter 3: Kinematics in Two Dimensions The only thing in life that is achieved without effort is failure. Source unknown "We are what we repeatedly do. Excellence, therefore, is not an act,
More informationTrigonometry Basics. Which side is opposite? It depends on the angle. θ 2. Y is opposite to θ 1 ; Y is adjacent to θ 2.
Trigonometry Basics Basic Terms θ (theta) variable for any angle. Hypotenuse longest side of a triangle. Opposite side opposite the angle (θ). Adjacent side next to the angle (θ). Which side is opposite?
More informationChapter 3. Table of Contents. Section 1 Introduction to Vectors. Section 2 Vector Operations. Section 3 Projectile Motion. Section 4 Relative Motion
Two-Dimensional Motion and Vectors Table of Contents Section 1 Introduction to Vectors Section 2 Vector Operations Section 3 Projectile Motion Section 4 Relative Motion Section 1 Introduction to Vectors
More informationVectors and Scalars. Scalar: A quantity specified by its magnitude only Vector: A quantity specified both by its magnitude and direction.
Vectors and Scalars Scalar: A quantity specified by its magnitude only Vector: A quantity specified both by its magnitude and direction. To distinguish a vector from a scalar quantity, it is usually written
More informationPhysics 40 Chapter 3: Vectors
Physics 40 Chapter 3: Vectors Cartesian Coordinate System Also called rectangular coordinate system x-and y- axes intersect at the origin Points are labeled (x,y) Polar Coordinate System Origin and reference
More informationBell Ringer: What is constant acceleration? What is projectile motion?
Bell Ringer: What is constant acceleration? What is projectile motion? Can we analyze the motion of an object on the y-axis independently of the object s motion on the x-axis? NOTES 3.2: 2D Motion: Projectile
More information4 MOTION IN TWO AND THREE DIMENSIONS
Chapter 4 Motion in Two and Three Dimensions 157 4 MOTION IN TWO AND THREE DIMENSIONS Figure 4.1 The Red Arrows is the aerobatics display team of Britain s Royal Air Force. Based in Lincolnshire, England,
More information170 Test example problems CH1,2,3
170 Test example problems CH1,2,3 WARNING: these are simply examples that showed up in previous semesters test. It does NOT mean that similar problems will be present in THIS semester s test. Hence, you
More informationTwo-Dimensional Motion Worksheet
Name Pd Date Two-Dimensional Motion Worksheet Because perpendicular vectors are independent of each other we can use the kinematic equations to analyze the vertical (y) and horizontal (x) components of
More informationVectors for Physics. AP Physics C
Vectors for Physics AP Physics C A Vector is a quantity that has a magnitude (size) AND a direction. can be in one-dimension, two-dimensions, or even three-dimensions can be represented using a magnitude
More informationWhen we throw a ball :
PROJECTILE MOTION When we throw a ball : There is a constant velocity horizontal motion And there is an accelerated vertical motion These components act independently of each other PROJECTILE MOTION A
More informationVectors. Vectors. Vectors. Reminder: Scalars and Vectors. Vector Practice Problems: Odd-numbered problems from
Vectors Vector Practice Problems: Odd-numbered problems from 3.1-3.21 Reminder: Scalars and Vectors Vector: Scalar: A number (magnitude) with a direction. Just a number. I have continually asked you, which
More informationVectors. Introduction
Chapter 3 Vectors Vectors Vector quantities Physical quantities that have both numerical and directional properties Mathematical operations of vectors in this chapter Addition Subtraction Introduction
More informationChapter 4 Kinematics II: Motion in Two and Three Dimensions
Chapter 4 Kinematics II: Motion in Two and Three Dimensions Demonstrations: 1) Ball falls down and another falls out 2) Parabolic and straight line motion from two different frames. The truck with a dropping
More informationChapter 3 Homework Packet. Conceptual Questions
Chapter 3 Homework Packet Conceptual Questions 1) Which one of the following is an example of a vector quantity? A) mass B) area C) distance D) velocity A vector quantity has both magnitude and direction.
More information(a) On the diagram above, draw an arrow showing the direction of velocity of the projectile at point A.
QUESTION 1 The path of a projectile in a uniform gravitational field is shown in the diagram below. When the projectile reaches its maximum height, at point A, its speed v is 8.0 m s -1. Assume g = 10
More informationOmm Al-Qura University Dr. Abdulsalam Ai LECTURE OUTLINE CHAPTER 3. Vectors in Physics
LECTURE OUTLINE CHAPTER 3 Vectors in Physics 3-1 Scalars Versus Vectors Scalar a numerical value (number with units). May be positive or negative. Examples: temperature, speed, height, and mass. Vector
More information2-D Vector Equations have the same form as 1-D Kinematics. f i i
2-D Vector Equations have the same form as 1-D Kinematics v = v + at f i 1 r = r + v t+ at f i i 2 2 2-D Vector Equations have the same form as 1-D Kinematics v = viˆ+ v ˆj f x y = ( v + ati ) ˆ+ ( v +
More informationChapter 2 A Mathematical Toolbox
Chapter 2 Mathematical Toolbox Vectors and Scalars 1) Scalars have only a magnitude (numerical value) Denoted by a symbol, a 2) Vectors have a magnitude and direction Denoted by a bold symbol (), or symbol
More informationProjectile Motion. v a = -9.8 m/s 2. Good practice problems in book: 3.23, 3.25, 3.27, 3.29, 3.31, 3.33, 3.43, 3.47, 3.51, 3.53, 3.
v a = -9.8 m/s 2 A projectile is anything experiencing free-fall, particularly in two dimensions. 3.23, 3.25, 3.27, 3.29, 3.31, 3.33, 3.43, 3.47, 3.51, 3.53, 3.55 Projectile Motion Good practice problems
More informationISSUED BY K V - DOWNLOADED FROM KINEMATICS
KINEMATICS *rest and Motion are relative terms, nobody can exist in a state of absolute rest or of absolute motion. *One dimensional motion:- The motion of an object is said to be one dimensional motion
More informationIn the real world, objects don t just move back and forth in 1-D! Projectile
Phys 1110, 3-1 CH. 3: Vectors In the real world, objects don t just move back and forth in 1-D In principle, the world is really 3-dimensional (3-D), but in practice, lots of realistic motion is 2-D (like
More informationGraphical Vector Addition
Vectors Chapter 4 Vectors and Scalars Measured quantities can be of two types Scalar quantities: only require magnitude (and proper unit) for description. Examples: distance, speed, mass, temperature,
More informationLesson 2. Physics 168. Luis Anchordoqui
Lesson 2 Physics 168 Luis Anchordoqui Deriving Constant-Acceleration Kinematic Equations To obtain an equation for position as a function of time! look at special case of motion with constant velocity!
More informationMotion in a 2 and 3 dimensions Ch 4 HRW
Motion in a and 3 dimensions Ch 4 HRW Motion in a plane D Motion in space 3D Projectile motion Position and Displacement Vectors A position vector r extends from a reference point (usually the origin O)
More informationINTRODUCTION AND KINEMATICS. Physics Unit 1 Chapters 1-3
INTRODUCTION AND KINEMATICS Physics Unit 1 Chapters 1-3 This Slideshow was developed to accompany the textbook OpenStax Physics Available for free at https://openstaxcollege.org/textbooks/college-physics
More informationFull file at
Section 3-1 Constructing Complex Motions from Simple Motion *1. In Figure 3-1, the motion of a spinning wheel (W) that itself revolves in a circle is shown. Which of the following would not be represented
More informationChapter 3: Vectors and Projectile Motion
Chapter 3: Vectors and Projectile Motion Vectors and Scalars You might remember from math class the term vector. We define a vector as something with both magnitude and direction. For example, 15 meters/second
More informationKinematics. Vector solutions. Vectors
Kinematics Study of motion Accelerated vs unaccelerated motion Translational vs Rotational motion Vector solutions required for problems of 2- directional motion Vector solutions Possible solution sets
More informationUnits. EMU Physics Department. Ali ÖVGÜN.
Units Ali ÖVGÜN EMU Physics Department www.aovgun.com 1 mile = 1609 m January 22-25, 2013 January 22-25, 2013 Vectors Ali ÖVGÜN EMU Physics Department www.aovgun.com Example 1: Operations with Vectors
More informationProjectile Motion. Practice test Reminder: test Feb 8, 7-10pm! me if you have conflicts! Your intuitive understanding of the Physical world
v a = -9.8 m/s Projectile Motion Good practice problems in book: 3.3, 3.5, 3.7, 3.9, 3.31, 3.33, 3.43, 3.47, 3.51, 3.53, 3.55 Practice test Reminder: test Feb 8, 7-10pm! Email me if you have conflicts!
More informationPhys101-T121-First Major Exam Zero Version, choice A is the correct answer
Phys101-T121-First Major Exam Zero Version, choice A is the correct answer Q1. Find the mass of a solid cylinder of copper with a radius of 5.00 cm and a height of 10.0 inches if the density of copper
More informationVectors. Scalars & vectors Adding displacement vectors. What about adding other vectors - Vector equality Order does not matter: i resultant A B
Vectors Scalars & vectors Adding displacement vectors i resultant f What about adding other vectors - Vector equality Order does not matter: B C i A A f C B A B Vector addition I Graphical vector addition
More informationBSP1153 Mechanics & Thermodynamics. Vector
BSP1153 Mechanics & Thermodynamics by Dr. Farah Hanani bt Zulkifli Faculty of Industrial Sciences & Technology farahhanani@ump.edu.my Chapter Description Expected Outcomes o To understand the concept of
More informationAP Physics First Nine Weeks Review
AP Physics First Nine Weeks Review 1. If F1 is the magnitude of the force exerted by the Earth on a satellite in orbit about the Earth and F2 is the magnitude of the force exerted by the satellite on the
More informationKINEMATICS OF A PARTICLE. Prepared by Engr. John Paul Timola
KINEMATICS OF A PARTICLE Prepared by Engr. John Paul Timola Particle has a mass but negligible size and shape. bodies of finite size, such as rockets, projectiles, or vehicles. objects can be considered
More information2D Kinematics. Note not covering scalar product or vector product right now we will need it for material in Chap 7 and it will be covered then.
Announcements: 2D Kinematics CAPA due at 10pm tonight There will be the third CAPA assignment ready this evening. Chapter 3 on Vectors Note not covering scalar product or vector product right now we will
More informationVectors. Vector Practice Problems: Odd-numbered problems from
Vectors Vector Practice Problems: Odd-numbered problems from 3.1-3.21 After today, you should be able to: Understand vector notation Use basic trigonometry in order to find the x and y components of a
More information2. KINEMATICS. By Liew Sau Poh
2. KINEMATICS By Liew Sau Poh 1 OBJECTIVES 2.1 Linear motion 2.2 Projectiles 2.3 Free falls and air resistance 2 OUTCOMES Derive and use equations of motion with constant acceleration Sketch and use the
More informationLab 5: Projectile Motion
Concepts to explore Scalars vs. vectors Projectiles Parabolic trajectory As you learned in Lab 4, a quantity that conveys information about magnitude only is called a scalar. However, when a quantity,
More informationB C = B 2 + C 2 2BC cosθ = (5.6)(4.8)cos79 = ) The components of vectors B and C are given as follows: B x. = 6.
1) The components of vectors B and C are given as follows: B x = 6.1 C x = 9.8 B y = 5.8 C y = +4.6 The angle between vectors B and C, in degrees, is closest to: A) 162 B) 111 C) 69 D) 18 E) 80 B C = (
More informationPHYS 101 Previous Exam Problems. Kinetic Energy and
PHYS 101 Previous Exam Problems CHAPTER 7 Kinetic Energy and Work Kinetic energy Work Work-energy theorem Gravitational work Work of spring forces Power 1. A single force acts on a 5.0-kg object in such
More informationModule 17: Systems, Conservation of Momentum and Center of Mass
Module 17: Systems, Conservation of Momentum and Center of Mass 17.1 External and Internal Forces and the Change in Momentum of a System So far we have restricted ourselves to considering how the momentum
More informationWork and Kinetic Energy
Lecture 12 Chapter 9 Work and Kinetic Energy I am sick and tired of your forces!!! Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi IN THIS CHAPTER, you will learn how to solve problems
More informationacceleration versus time. LO Determine a particle s change in position by graphical integration on a graph of velocity versus time.
Chapter: Chapter 2 Learning Objectives LO 2.1.0 Solve problems related to position, displacement, and average velocity to solve problems. LO 2.1.1 Identify that if all parts of an object move in the same
More informationUnit 1, Lessons 2-5: Vectors in Two Dimensions
Unit 1, Lessons 2-5: Vectors in Two Dimensions Textbook Sign-Out Put your name in it and let s go! Check-In Any questions from last day s homework? Vector Addition 1. Find the resultant displacement
More informationMotion in Two and Three Dimensions
PH 1-1D Spring 013 Motion in Two and Three Dimensions Lectures 5,6,7 Chapter 4 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition) 1 Chapter 4 Motion in Two and Three Dimensions In this chapter
More informationLecture PowerPoints. Chapter 3 Physics for Scientists & Engineers, with Modern Physics, 4 th edition Giancoli
Lecture PowerPoints Chapter 3 Physics for Scientists & Engineers, with Modern Physics, 4 th edition Giancoli 2009 Pearson Education, Inc. This work is protected by United States copyright laws and is provided
More informationVectors. However, cartesian coordinates are really nothing more than a way to pinpoint an object s position in space
Vectors Definition of Scalars and Vectors - A quantity that requires both magnitude and direction for a complete description is called a vector quantity ex) force, velocity, displacement, position vector,
More informationPhys101 First Major-061 Zero Version Coordinator: Abdelmonem Monday, October 30, 2006 Page: 1
Coordinator: Abdelmonem Monday, October 30, 006 Page: 1 Q1. An aluminum cylinder of density.70 g/cm 3, a radius of.30 cm, and a height of 1.40 m has the mass of: A) 6.8 kg B) 45.1 kg C) 13.8 kg D) 8.50
More information