1. Units and Prefixes


 Aubrie Clarke
 2 years ago
 Views:
Transcription
1
2 1. Units and Prefixes SI units Units must accompany quantities at all times, otherwise the quantities are meaningless. If a person writes mass = 1, do they mean 1 gram, 1 kilogram or 1 tonne? The Système International d Unitè (SI) system of units is used by modern scientists worldwide and all equations and constants are defined in terms of this system of units. When substituting numbers into equations, you must make sure that the quantities are in SI units. Your answers will also be in SI units, and the units are part of the answer, otherwise the answer is meaningless. The SI units system uses fundamental units, which include the: metre (m) to measure length kilogram (kg) to measure mass second (s) to measure time These quantities are fundamental because they cannot be expressed in terms of other quantities. Note that even though a centimetre, millimetre and gram are related to metres and kilograms, they are NOT SI units. You must always use metres for length and kilograms for mass. Copyright MATRIX EDUCATION 2014 Page 10 of 199 Our Students Come First!
3 The SI units also include derived units used to describe other quantities that are used in science. These units can be expressed in terms of the fundamental units. Some units you will encounter in this course are: Quantity Units SI Units Equivalent SI Units Speed Metres per second (ms 1 ) Acceleration Metres per second squared (ms 2 ) Force Newton (N) (kg ms 2 ) Energy Joule (J) (kg m 2 s 2 ) Momentum Kilograms metres per second (kg ms 1 ) Impulse Newton Seconds (Ns) (kg ms 1 ) Prefixes are commonly used to indicate the size of a quantity, e.g. 1 kilometre or 1 megabyte. A kilometre is 1000 metres; the prefix kilo means one thousand and a megabyte is one million bytes; the prefix mega means one million. If a quantity is given using a prefix, you must multiply it by the appropriate factor to convert it to SI units before using it in calculations. Prefix Symbol Factor Giga G x 10 9 (billion) Mega M x 10 6 (million) Kilo K x 10 3 (thousand) Centi C x 102 (one hundredth) Milli m x 103 (one thousandth) Micro μ x 106 (one millionth) Nano n x 109 (one billionth) Copyright MATRIX EDUCATION 2014 Page 11 of 199 Our Students Come First!
4 2. Scalars and Vectors Students learn to: distinguish between scalar and vector quantities in equations Definitions Physics is a science based on measurement. Some things are measurable, like physical quantities, and some aren t. Physical quantities, things we can measure, can be separated into two main categories scalars and vectors. A scalar is any measurement that has a magnitude but doesn t have a direction. A scalar requires only a number and a unit to be complete. Mathematically, all scalars can be considered the same. Mass and area are examples of scalar quantities. Australia has an area of 7,617,930m 2. A vector is any quantity that has a magnitude and a direction associated with it. We say a city is 1000 km south or a car travels at 60 km/h east. Mathematically, all vectors are the same, but vectors are different to scalars. Classify the following quantities as either scalars or vectors: Distance (d), displacement (r ), acceleration (a ), speed (v), mass (m), impulse (I ) time (t), force (F ), energy (E), power (P), momentum (p ), velocity (v ) SCALAR VECTOR Copyright MATRIX EDUCATION 2014 Page 12 of 199 Our Students Come First!
5 An arrow above a letter or boldface type is often used to indicate a vector quantity. When working with scalars, the mathematics we know will suffice. However, because directions are involved in vectors, they need their own version of mathematics for operations such as addition, subtraction, decomposition, multiplication, division and so forth. We will now look into a few types of vector operations. Vector representation Vector quantities can be added, but first we must learn how to represent them. N θ x Vectors are normally represented as arrows, as shown above. In a vector: The length of the line, x, represents the magnitude of the vector in some units. The arrow gives the direction and has a head and a tail. The head points in the specified direction. The magnitude (x), units and direction (θ) are clearly labelled. In the space below, draw a scaled diagram representing the vector 5 cm N40 W, clearly labelling all important details. Copyright MATRIX EDUCATION 2014 Page 13 of 199 Our Students Come First!
6 Vector addition The resultant vector is the vector that results from the joining of two or more vectors, headtotail. v 1 + v 2 The steps for the vector addition of two vectors v 1 and v 2 is outlined below: 1) Choose an origin and sketch one of the vectors, v 1. N v 1 2) Join the tail of the second vector, v 2, to the head of the first vector. N v 1 v 2 3) Connect the tail of the first vector to the head of the second vector. This is the resultant vector, v 1 + v 2. N v 1 v 2 v 1 + v 2 Copyright MATRIX EDUCATION 2014 Page 14 of 199 Our Students Come First!
7 4) Determine the magnitude and direction of the resultant vector using accurate scale drawings and trigonometry methods. Pythagoras Theorem Cosine rule (a 2 = b 2 + c 2 2bc cos A) N θ v 1 v 2 v 1 + v 2 DEMONSTRATION: Vector addition simulator. Which of the following show the vector addition diagrams matched correctly to the respective vector addition equations? I II III IV A C C A B A A B B B C C I II III IV A+C=B A+B=C A+B=C A+B=C C+B=A C+A=B C+B=A A+C=B A+C=B A+C=B A+B=C A+B=C A+C=B B+A=C B+A=B C+A=B Copyright MATRIX EDUCATION 2014 Page 15 of 199 Our Students Come First!
8 Find the resultant vector of the addition of the following vectors. In each case show the vector addition. a) v 1 = 10 m/s East and v 2 = 30 m/s East. 3 b) There are two forces on a toy wagon, F 1 = 15 N East and F 2 = 25 N North. 4 c) Hazel takes thirty steps West, twentytwo steps North, fortyfour steps East, and twentynine steps South. Assume all her steps are the same size. How many steps would she have to take from her starting point to end in the same spot if she had gone directly? In what direction would she have to walk? 5 Copyright MATRIX EDUCATION 2014 Page 16 of 199 Our Students Come First!
9 Vector decomposition It is useful to think of a vector as the sum of two other vectors at right angles to each other. These two vectors are called components of the original vector. Consider the figure shown below. v vy vx = + vy vx v y is a component of a vector v in the vertical direction. Express v y in terms of and v. 6 v x is a component of a vector v in the horizontal direction. Express v x in terms of and v. 7 The vectors w and y below can be decomposed into vertical components (w y, y y) and horizontal components (w x, y x). Draw and label these components. θ y w θ Copyright MATRIX EDUCATION 2014 Page 17 of 199 Our Students Come First!
10 The figure shown below is a diagram of the addition of two vectors, v 1 and v 2. The dotted vector v R is the result vector. vr The vectors v 1 and v 2 can be decomposed. The components are shown. We can use the components of the two vectors to find the resultant vector, v R. 8sin10 vr N 10sin30 10cos30 8cos10 Copyright MATRIX EDUCATION 2014 Page 18 of 199 Our Students Come First!
11 To determine the magnitude of the resultant vector, we use Pythagoras Theorem: v R = (10cos30 + 8cos10) 2 + (10sin30 + 8sin10) 2 = 8 To determine the direction of the resultant vector: tanθ = Opposite 10sin30 + 8sin10 = Adjacent 10cos30 + 8cos10 θ = 9 Therefore, v R = N E Remember, when giving the direction of the resultant vector, you must give the angle between the vector and the vertical line joining North and South. NOTE TO STUDENTS There are two common ways used to state a direction: as a true bearing or a compass bearing. True bearing is measured in a clockwise direction from the North and given in a standard threedigit notation. Compass bearings are directions given from the North or the South. For example, a true bearing of 135 is equivalent to the compass bearing S45 E. DID YOU KNOW? The function Pol(x,y) on your Casio calculator can quickly determine the length of the hypotenuse and the adjacent angle in a right angled triangle. Copyright MATRIX EDUCATION 2014 Page 19 of 199 Our Students Come First!
12 Find the resultant of the two vectors using the method of components. In each case, make a rough sketch of the vector addition and the vector components. v 1 = 15 m/s N30 E and v 2 = 25 m/s N45 E v 1 = 15 m/s N45 E and v 2 = 25 m/s S30 E Copyright MATRIX EDUCATION 2014 Page 20 of 199 Our Students Come First!
13 Vector subtraction Just as we can add vectors, we can also subtract them. Vector subtraction is an operation that is important in relative motion, which we will discuss later. When we subtract two vectors, v 2 v 1, it is equivalent to adding two vectors, v 2 + ( v 1). What is the meaning of the vector v 1? v 1 is a vector equal in magnitude to v 1 but opposite in direction to it. See the figure below. v1 v1 Vectors v 2 and v 2 are shown below. v2 v2 An example of vector subtraction is shown below. v1 v2 v1 = + v2 = v1 v2 Copyright MATRIX EDUCATION 2014 Page 21 of 199 Our Students Come First!
14 Subtract the following vectors (v 2 v 1). In each case make a sketch of the vector subtraction. v 1 = 10 ms 1 East and v 2 = 30 ms 1 East 12 v 1 = 10 ms 1 East and v 2 = 30 ms 1 West 13 F 1 = 15 N East and F 2 = 25 N South [F 2 F 1] 14 Copyright MATRIX EDUCATION 2014 Page 22 of 199 Our Students Come First!
15 3. Distance & Displacement Distance (r) [m] Distance is a scalar quantity. It refers to the length of the entire path travelled by a body. The SI unit for distance is metres (m). Displacement (r ) [m + direction] Displacement is a vector quantity. It refers to the change in position of a body, or the difference between where you started and where you end. Displacement is specified by both magnitude (m) and direction. The difference between distance and displacement is illustrated below. Source: A displacement and the distance travelled can be of the same magnitude. Give an example of when this could be the case. 15 However, since displacement gives information about the overall result, it must include the direction of the finishing point from the starting point. Displacement can be zero even if the distance travelled is very large. Copyright MATRIX EDUCATION 2014 Page 23 of 199 Our Students Come First!
16 Consider the following example. A bee leaves its hive to gather nectar. Its journey takes it 200 m due north from the hive, then 100 m due east, then 300 m due south and then finally on a beeline straight back to the hive. Draw a scale diagram of the bee s journey. Determine the distance travelled by the bee. 17 Determine the bee s displacement at the end of its journey. 18 Copyright MATRIX EDUCATION 2014 Page 24 of 199 Our Students Come First!
17 4. Lesson Review Questions A car travels 40 km south and then 30 km west in 1 hour. What is the total distance travelled? What is the car s straightline distance from its starting point at the end of the hour? What is the car s total displacement? While on holidays, Sabiha drives 140 km northwest to visit the Hunter Valley and then 260 km S30 o E to go surfing in Wollongong. Draw a diagram to represent this journey. What is the total distance she travelled that day? What is her final displacement? Copyright MATRIX EDUCATION 2014 Page 25 of 199 Our Students Come First!
18 Jackson takes 2 minutes to jog 500 m east, then 3 minutes to jog 800 m west, then 5 minutes to return home. Draw a diagram to represent his journey. What is the total distance travelled? What is his displacement after 2 minutes? What is his displacement after 5 minutes? What is his displacement after 10 minutes? Copyright MATRIX EDUCATION 2014 Page 26 of 199 Our Students Come First!
19 Subtract the following vectors (a 2 a 1), making a sketch of the vector subtraction. a 1= 10 ms 2 N45 E and a 2 = 8 ms 2 West Copyright MATRIX EDUCATION 2014 Page 27 of 199 Our Students Come First!
20 ANSWERS 3 40 m/s East N N31 E (16 steps) S63 E 6 vy = vsinθ 7 vx = vcosθ m/s N39 E m/s S64 E ms 1 East ms 1 West N N31 W 15 A ball rolled on a horizontal surface in a straight line. 17 Distance travelled = = m 18 0 m. It starts and ends its journey at the same point (its hive). Copyright MATRIX EDUCATION 2014 Page 28 of 199 Our Students Come First!
AS Physics INDUCTION WORK XKCD. Student. Class 12 A / B / C / D Form
AS Physics 201415 INDUCTION WORK XKCD Student Class 12 A / B / C / D Form MCC 2014 1. Physical Quantities Maths and Physics have an important but overlooked distinction by students. Numbers in Physics
More informationIntroduction to Vectors
Introduction to Vectors A vector is a physical quantity that has both magnitude and direction. An example is a plane flying NE at 200 km/hr. This vector is written as 200 Km/hr at 45. Another example is
More informationVectors are quantities that have both a direction and a magnitude (size).
Scalars & Vectors Vectors are quantities that have both a direction and a magnitude (size). Ex. km, 30 ο north of east Examples of Vectors used in Physics Displacement Velocity Acceleration Force Scalars
More informationFigure 1.1 Vector A and Vector F
CHAPTER I VECTOR QUANTITIES Quantities are anything which can be measured, and stated with number. Quantities in physics are divided into two types; scalar and vector quantities. Scalar quantities have
More informationPHYSICS Unit 1A Kinematics 1
PHYSICS 2204 Unit 1A Kinematics 1 SI Units Metric Prefixes Factor Prefix Symbol 10 12 tera T 10 9 giga G 10 6 mega M 10 3 kilo k 10 2 hecto h 10 0 Standard unit  101 deci d 102 centi c 103 milli
More information1.3 Displacement in Two Dimensions
1.3 Displacement in Two Dimensions So far, you have learned about motion in one dimension. This is adequate for learning basic principles of kinematics, but it is not enough to describe the motions of
More informationSummary Notes. to avoid confusion it is better to write this formula in words. time
National 4/5 Physics Dynamics and Space Summary Notes The coloured boxes contain National 5 material. Section 1 Mechanics Average Speed Average speed is the distance travelled per unit time. distance (m)
More informationPHYSICS 151 Notes for Online Lecture #6
PHYSICS 151 Notes for Online Lecture #6 Vectors  A vector is basically an arrow. The length of the arrow represents the magnitude (value) and the arrow points in the direction. Many different quantities
More informationPhysical Quantities and Units
Physical Quantities and Units 1 Revision Objectives This chapter will explain the SI system of units used for measuring physical quantities and will distinguish between vector and scalar quantities. You
More informationBROCK UNIVERSITY. PHYS 1P21/1P91 Solutions to Midterm test 26 October 2013 Instructor: S. D Agostino
BROCK UNIVERSITY PHYS 1P21/1P91 Solutions to Midterm test 26 October 2013 Instructor: S. D Agostino 1. [10 marks] Clearly indicate whether each statement is TRUE or FALSE. Then provide a clear, brief,
More informationScientific Notation, Engineering Notation
Scientific, Engineering Scientific Scientific or Standard Form is a way of writing numbers in a compact form. A number written in Scientific is expressed as a number from 1 to less than multiplied by a
More informationDifference between a vector and a scalar quantity. N or 90 o. S or 270 o
Vectors Vectors and Scalars Distinguish between vector and scalar quantities, and give examples of each. method. A vector is represented in print by a bold italicized symbol, for example, F. A vector has
More informationExamples of Scalar and Vector Quantities 1. Candidates should be able to : QUANTITY VECTOR SCALAR
Candidates should be able to : Examples of Scalar and Vector Quantities 1 QUANTITY VECTOR SCALAR Define scalar and vector quantities and give examples. Draw and use a vector triangle to determine the resultant
More informationLecture 4. Vectors. Motion and acceleration in two dimensions. Cutnell+Johnson: chapter ,
Lecture 4 Vectors Motion and acceleration in two dimensions Cutnell+Johnson: chapter 1.51.8, 3.13.3 We ve done motion in one dimension. Since the world usually has three dimensions, we re going to do
More informationMechanics 1. Revision Notes
Mechanics 1 Revision Notes July 2012 MECHANICS 1... 2 1. Mathematical Models in Mechanics... 2 Assumptions and approximations often used to simplify the mathematics involved:... 2 2. Vectors in Mechanics....
More informationMATHEMATICAL VECTOR ADDITION
MATHEMATICAL VECTOR ADDITION Part One: The Basics When combining two vectors that act at a right angle to each other, you are able to use some basic geometry to find the magnitude and direction of the
More informationUnit 1: Vectors. a m/s b. 8.5 m/s c. 7.2 m/s d. 4.7 m/s
Multiple Choice Portion 1. A boat which can travel at a speed of 7.9 m/s in still water heads directly across a stream in the direction shown in the diagram above. The water is flowing at 3.2 m/s. What
More informationVECTORS. A vector is a quantity that has both magnitude and direction.
VECTOS Definition: A vector is a quantity that has both magnitude and direction. NOTE: The position of a vector has no bearing on its definition. A vector can be slid horizontally or vertically without
More information2. Right Triangle Trigonometry
2. Right Triangle Trigonometry 2.1 Definition II: Right Triangle Trigonometry 2.2 Calculators and Trigonometric Functions of an Acute Angle 2.3 Solving Right Triangles 2.4 Applications 2.5 Vectors: A Geometric
More informationUnits and Vectors: Tools for Physics
Chapter 1 Units and Vectors: Tools for Physics 1.1 The Important Stuff 1.1.1 The SI System Physics is based on measurement. Measurements are made by comparisons to well defined standards which define the
More informationVector Lab Teacher s Guide
Vector Lab Teacher s Guide Objectives: 1. Use s to show addition of force vectors. 2. Vector addition using tiptotail method and trigonometry. Materials: Each group must have: 2 ring stands, 2 s, 4 washers,
More information1.4 Velocity and Acceleration in Two Dimensions
Figure 1 An object s velocity changes whenever there is a change in the velocity s magnitude (speed) or direction, such as when these cars turn with the track. 1.4 Velocity and Acceleration in Two Dimensions
More informationSolving Simultaneous Equations and Matrices
Solving Simultaneous Equations and Matrices The following represents a systematic investigation for the steps used to solve two simultaneous linear equations in two unknowns. The motivation for considering
More informationIntroduction and Mathematical Concepts
CHAPTER 1 Introduction and Mathematical Concepts PREVIEW In this chapter you will be introduced to the physical units most frequently encountered in physics. After completion of the chapter you will be
More information6. Vectors. 1 20092016 Scott Surgent (surgent@asu.edu)
6. Vectors For purposes of applications in calculus and physics, a vector has both a direction and a magnitude (length), and is usually represented as an arrow. The start of the arrow is the vector s foot,
More informationLecture PowerPoints. Chapter 3 Physics: Principles with Applications, 6 th edition Giancoli
Lecture PowerPoints Chapter 3 Physics: Principles with Applications, 6 th edition Giancoli 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the
More informationA scalar quantity is fully described by its magnitude (size) and unit, e.g. time = 220 s. Force = 800 N upwards direction
Vector and Scalar Quantities (recap on National 5 Physics) A scalar quantity is fully described by its magnitude (size) and unit, e.g. quantity time = 220 s unit magnitude A vector quantity is fully described
More informationMotion Lesson 1: Review of Basic Motion
Motion in one and two dimensions: Lesson 1 Seminotes Motion Lesson 1: Review of Basic Motion Note. For these semi notes we will use the bold italics convention to represent vectors. Complete the following
More informationSUMMING VECTOR QUANTITIES USING PARALELLOGRAM METHOD
EXPERIMENT 2 SUMMING VECTOR QUANTITIES USING PARALELLOGRAM METHOD Purpose : Summing the vector quantities using the parallelogram method Apparatus: Different masses between 11000 grams A flat wood, Two
More informationBasic Electrical Theory
Basic Electrical Theory Mathematics Review PJM State & Member Training Dept. Objectives By the end of this presentation the Learner should be able to: Use the basics of trigonometry to calculate the different
More informationLab 2: Vector Analysis
Lab 2: Vector Analysis Objectives: to practice using graphical and analytical methods to add vectors in two dimensions Equipment: Meter stick Ruler Protractor Force table Ring Pulleys with attachments
More informationwww.parklandsd.org/web/physics/
Course: AP Physics 1 2016 2017 Physics Teachers: Mrs. Dogmanits & Mr. Wetherhold Summer Assignment DO NOT TAKE A TEXTBOOK FROM THE LIBRARY! USE THE ONLINE TEXT. 1. The AP Physics 1 textbook is available
More informationLesson 5 Rotational and Projectile Motion
Lesson 5 Rotational and Projectile Motion Introduction: Connecting Your Learning The previous lesson discussed momentum and energy. This lesson explores rotational and circular motion as well as the particular
More informationGeneral Physics 1. Class Goals
General Physics 1 Class Goals Develop problem solving skills Learn the basic concepts of mechanics and learn how to apply these concepts to solve problems Build on your understanding of how the world works
More informationConcept Review. Physics 1
Concept Review Physics 1 Speed and Velocity Speed is a measure of how much distance is covered divided by the time it takes. Sometimes it is referred to as the rate of motion. Common units for speed or
More informationectors and Application P(x, y, z)! $ ! $ & " 11,750 12,750 13,750
thstrack MathsTrack (NOTE Feb 2013: This is the old version of MathsTrack. New books will be created during 2013 and 2014) odule 3 Topic 3 Module 9 Introduction Vectors and Applications to Matrices ectors
More informationSpeed, velocity and acceleration
Chapter Speed, velocity and acceleration Figure.1 What determines the maximum height that a polevaulter can reach? 1 In this chapter we look at moving bodies, how their speeds can be measured and how
More informationChapter 1 Concepts of Motion and Mathematical Background
Chapter 1 Concepts of Motion and Mathematical Background Topics: Motion diagrams Position and time Velocity Scientific notation and units Vectors and motion Sample question: As this snowboarder moves in
More informationCartesian Coordinate System. Also called rectangular coordinate system x and y axes intersect at the origin Points are labeled (x,y)
Physics 1 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 line
More informationModule 2.1. Introduction to S.I units
Module 2.1 Introduction to S.I units Learning Outcomes On successful completion of this module learners will be able to  Describe some of the S.I units relevant to energy use in buildings. S.I = The International
More informationA physical quantity is any quantity that can be measured with a certain mathematical precision. Example: Force
1 Unit Systems Conversions Powers of Physical Quantities Dimensions Dimensional Analysis Scientific Notation Computer Notation Calculator Notation Significant Figures Math Using Significant Figures Order
More informationMathematics (Project Maths Phase 1)
2011. S133S Coimisiún na Scrúduithe Stáit State Examinations Commission Junior Certificate Examination Sample Paper Mathematics (Project Maths Phase 1) Paper 2 Ordinary Level Time: 2 hours 300 marks Running
More informationPHYSICS 149: Lecture 4
PHYSICS 149: Lecture 4 Chapter 2 2.3 Inertia and Equilibrium: Newton s First Law of Motion 2.4 Vector Addition Using Components 2.5 Newton s Third Law 1 Net Force The net force is the vector sum of all
More informationNational 5 Physics. Dynamics and Space
National 5 Physics Dynamics and Space NASA www.rcairplaneworld.com Millburn Academy National 5 Physics: Dynamics and Space Adapted from George Watson s College 1 Prefixes and Scientific Notation Throughout
More informationChapter 4. Forces and Newton s Laws of Motion
Chapter 4 Forces and Newton s Laws of Motion 4.1 The Concepts of Force and Mass A force is a push or a pull. Contact forces arise from physical contact. Actionatadistance forces do not require contact
More informationMeasurements 1. BIRKBECK MATHS SUPPORT www.mathsupport.wordpress.com. In this section we will look at. Helping you practice. Online Quizzes and Videos
BIRKBECK MATHS SUPPORT www.mathsupport.wordpress.com Measurements 1 In this section we will look at  Examples of everyday measurement  Some units we use to take measurements  Symbols for units and converting
More informationat v = u + 2as 6. Carry out calculations using the above kinematic relationships.
MECHANICS AND PROPERTIES OF MATTER The knowledge and understanding content for this unit is given below. Vectors 1. Distinguish between distance and displacement. 2. Distinguish between speed and velocity.
More informationNCEA Level 1 Numeracy  Measurement Conversions within the metric measurement system
NCEA Level 1 Numeracy  Measurement Conversions within the metric measurement system Content This resource supports the teaching and learning of conversions within the metric measurement system. The sequence
More informationReview of Scientific Notation and Significant Figures
II1 Scientific Notation Review of Scientific Notation and Significant Figures Frequently numbers that occur in physics and other sciences are either very large or very small. For example, the speed of
More informationUnit 4: Science and Materials in Construction and the Built Environment. Chapter 14. Understand how Forces act on Structures
Chapter 14 Understand how Forces act on Structures 14.1 Introduction The analysis of structures considered here will be based on a number of fundamental concepts which follow from simple Newtonian mechanics;
More informationThe Importance of MEASUREMENT
Scientists use many skills as they investigate the world around them. They make observations by gathering information with their senses. Some observations are simple. For example, a simple observation
More informationWorked Examples from Introductory Physics Vol. I: Basic Mechanics. David Murdock Tenn. Tech. Univ.
Worked Examples from Introductory Physics Vol. I: Basic Mechanics David Murdock Tenn. Tech. Univ. February 24, 2005 2 Contents To the Student. Yeah, You. i 1 Units and Vectors: Tools for Physics 1 1.1
More informationLearning Outcomes. Distinguish between Distance and Displacement when comparing positions. Distinguish between Scalar and Vector Quantities
Dr Pusey Learning Outcomes Distinguish between Distance and Displacement when comparing positions Distinguish between Scalar and Vector Quantities Add and subtract vectors in one and two dimensions What
More informationLecture notes for Physics 10154: General Physics I. Hana Dobrovolny Department of Physics & Astronomy, Texas Christian University, Fort Worth, TX
Lecture notes for Physics 10154: General Physics I Hana Dobrovolny Department of Physics & Astronomy, Texas Christian University, Fort Worth, TX December 3, 2012 Contents 1 Introduction 5 1.1 The tools
More informationSCALAR VS. VECTOR QUANTITIES
SCIENCE 1206 MOTION  Unit 3 Slideshow 2 SPEED CALCULATIONS NAME: TOPICS OUTLINE SCALAR VS. VECTOR SCALAR QUANTITIES DISTANCE TYPES OF SPEED SPEED CALCULATIONS DISTANCETIME GRAPHS SPEEDTIME GRAPHS SCALAR
More information2016 Arizona State University Page 1 of 15
NAME: MATH REFRESHER ANSWER SHEET (Note: Write all answers on this sheet and the following graph page.) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.
More informationHomework 1: Exercise 1 Metric  English Conversion [based on the Chauffe & Jefferies (2007)]
MAR 110 HW 1: Exercise 1 Conversions p. 1 11. THE METRIC SYSTEM Homework 1: Exercise 1 Metric  English Conversion [based on the Chauffe & Jefferies (2007)] The French developed the metric system during
More informationChapter 3B  Vectors. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University
Chapter 3B  Vectors A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 2007 Vectors Surveyors use accurate measures of magnitudes and directions to
More informationMotion in One Dimension  Grade 10
Chapter 3 Motion in One Dimension  Grade 10 3.1 Introduction This chapter is about how things move in a straight line or more scientifically how things move in one dimension. This is useful for learning
More informationChapter 3 Kinematics in Two or Three Dimensions; Vectors. Copyright 2009 Pearson Education, Inc.
Chapter 3 Kinematics in Two or Three 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
More informationYear 5 Mathematics Programme of Study Maths worksheets from mathsphere.co.uk MATHEMATICS. Programme of Study. Year 5 Number and Place Value
MATHEMATICS Programme of Study Year 5 Number and Place Value Here are the statutory requirements: Number and place value read, write, order and compare numbers to at least 1 000 000 and determine the value
More informationAP Physics C Summer Assignment
AP Physics C Summer Assignment Welcome to AP Physics C! It is a college level physics course that is fun, interesting and challenging on a level you ve not yet experienced. This summer assignment will
More informationVector Definition. Chapter 1. Example 2 (Position) Example 1 (Position) Activity: What is the position of the center of your tabletop?
Vector Definition Chapter 1 Vectors A quantity that has two properties: magnitude and direction It is represented by an arrow; visually the length represents magnitude It is typically drawn on a coordinate
More informationUNIT 1 MASS AND LENGTH
UNIT 1 MASS AND LENGTH Typical Units Typical units for measuring length and mass are listed below. Length Typical units for length in the Imperial system and SI are: Imperial SI inches ( ) centimetres
More informationChapter 10: Terminology and Measurement in Biomechanics
Chapter 10: Terminology and Measurement in Biomechanics KINESIOLOGY Scientific Basis of Human Motion, 11th edition Hamilton, Weimar & Luttgens Presentation Created by TK Koesterer, Ph.D., ATC Humboldt
More information1Physical quantities and units
1Physical quantities and units By the end of this chapter you should be able to: explain what is meant by a in physics; state the five fundamental quantities recognised and used in physics; explain the
More informationEquilibrium of Concurrent Forces (Force Table)
Equilibrium of Concurrent Forces (Force Table) Objectives: Experimental objective Students will verify the conditions required (zero net force) for a system to be in equilibrium under the influence of
More informationAll About Motion  Displacement, Velocity and Acceleration
All About Motion  Displacement, Velocity and Acceleration Program Synopsis 2008 20 minutes Teacher Notes: Ian Walter Dip App Chem; GDipEd Admin; TTTC This program explores vector and scalar quantities
More informationChapter 4. Dynamics: Newton s Laws of Motion
Chapter 4 Dynamics: Newton s Laws of Motion The Concepts of Force and Mass A force is a push or a pull. Contact forces arise from physical contact. Actionatadistance forces do not require contact and
More informationPROBLEM SOLVING, REASONING, FLUENCY. Year 6 Term 1 Term 2 Term 3 Term 4 Term 5 Term 6 Number and Place Value. Measurement Four operations
PROBLEM SOLVING, REASONING, FLUENCY Year 6 Term 1 Term 2 Term 3 Term 4 Term 5 Term 6 Number and Place Value Addition and subtraction Large numbers Fractions & decimals Mental and written Word problems,
More informationNumber & Place Value. Addition & Subtraction. Digit Value: determine the value of each digit. determine the value of each digit
Number & Place Value Addition & Subtraction UKS2 The principal focus of mathematics teaching in upper key stage 2 is to ensure that pupils extend their understanding of the number system and place value
More informationDyffryn School Ysgol Y Dyffryn Mathematics Faculty
Dyffryn School Ysgol Y Dyffryn Mathematics Faculty Formulae and Facts Booklet Higher Tier Number Facts Sum This means add. Difference This means take away. Product This means multiply. Share This means
More informationMaths Area Approximate Learning objectives. Additive Reasoning 3 weeks Addition and subtraction. Number Sense 2 weeks Multiplication and division
Maths Area Approximate Learning objectives weeks Additive Reasoning 3 weeks Addition and subtraction add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar
More informationMATHS LEVEL DESCRIPTORS
MATHS LEVEL DESCRIPTORS Number Level 3 Understand the place value of numbers up to thousands. Order numbers up to 9999. Round numbers to the nearest 10 or 100. Understand the number line below zero, and
More informationAP Physics Course 1 Summer Assignment. Teachers: Mr. Finn, Mrs. Kelly, Mr. Simowitz, Mr. Slesinski
AP Physics Course 1 Summer Assignment Teachers: Mr. Finn, Mrs. Kelly, Mr. Simowitz, Mr. Slesinski On the following pages, there are six sections that use the basic skills that will be used throughout the
More informationSOLID MECHANICS DYNAMICS TUTORIAL INERTIA FORCES IN MECHANISMS
SOLID MECHANICS DYNAMICS TUTORIAL INERTIA FORCES IN MECHANISMS This work covers elements of the syllabus for the Engineering Council Exam D225 Dynamics of Mechanical Systems C103 Engineering Science. This
More informationSolution: 2. Sketch the graph of 2 given the vectors and shown below.
7.4 Vectors, Operations, and the Dot Product Quantities such as area, volume, length, temperature, and speed have magnitude only and can be completely characterized by a single real number with a unit
More informationOne advantage of this algebraic approach is that we can write down
. Vectors and the dot product A vector v in R 3 is an arrow. It has a direction and a length (aka the magnitude), but the position is not important. Given a coordinate axis, where the xaxis points out
More informationVector has a magnitude and a direction. Scalar has a magnitude
Vector has a magnitude and a direction Scalar has a magnitude Vector has a magnitude and a direction Scalar has a magnitude a brick on a table Vector has a magnitude and a direction Scalar has a magnitude
More information21 Position, Displacement, and Distance
21 Position, Displacement, and Distance In describing an object s motion, we should first talk about position where is the object? A position is a vector because it has both a magnitude and a direction:
More informationMathematics Teachers Enrichment Program MTEP 2012 Trigonometry and Bearings
Mathematics Teachers Enrichment Program MTEP 2012 Trigonometry and Bearings Trigonometry in Right Triangles A In right ABC, AC is called the hypotenuse. The vertices are labelled using capital letters.
More informationYear 5. Pupils should identify the place value in large whole numbers.
Year 5 Year 5 programme of study (statutory requirements) Number, place value, approximation and estimation Number, place value, approximation and estimation Pupils should identify the place value in large
More informationA vector is a directed line segment used to represent a vector quantity.
Chapters and 6 Introduction to Vectors A vector quantity has direction and magnitude. There are many examples of vector quantities in the natural world, such as force, velocity, and acceleration. A vector
More informationLab: Vectors. You are required to finish this section before coming to the lab. It will be checked by one of the lab instructors when the lab begins.
Lab: Vectors Lab Section (circle): Day: Monday Tuesday Time: 8:00 9:30 1:10 2:40 Name Partners PreLab You are required to finish this section before coming to the lab. It will be checked by one of the
More informationUnits represent agreed upon standards for the measured quantities.
Name Pd Date Chemistry Scientific Measurement Guided Inquiry Teacher s Notes Work with your group using your prior knowledge, the textbook (2.1 2.7), internet research, and class discussion to complete
More informationWhat is the SI system of measurement?
ALE 3. SI Units of Measure & Unit Conversions Name CHEM 161 K. Marr Team No. Section What is the SI system of measurement? The Model the International System of Units (Reference: Section 1.5 in Silberberg
More informationPHYSICS 151 Notes for Online Lecture #1
PHYSICS 151 Notes for Online Lecture #1 Whenever we measure a quantity, that measurement is reported as a number and a unit of measurement. We say such a quantity has dimensions. Units are a necessity
More informationA Review of Vector Addition
Motion and Forces in Two Dimensions Sec. 7.1 Forces in Two Dimensions 1. A Review of Vector Addition. Forces on an Inclined Plane 3. How to find an Equilibrant Vector 4. Projectile Motion Objectives Determine
More information81 Introduction to Vectors
State whether each quantity described is a vector quantity or a scalar quantity. 1. a box being pushed at a force of 125 newtons This quantity has a magnitude of 125 newtons, but no direction is given.
More informationPrinciples and Laws of Motion
2009 19 minutes Teacher Notes: Ian Walter DipAppChem; TTTC; GDipEdAdmin; MEdAdmin (part) Program Synopsis This program begins by looking at the different types of motion all around us. Forces that cause
More informationSection 9.1 Vectors in Two Dimensions
Section 9.1 Vectors in Two Dimensions Geometric Description of Vectors A vector in the plane is a line segment with an assigned direction. We sketch a vector as shown in the first Figure below with an
More informationREVIEW OVER VECTORS. A scalar is a quantity that is defined by its value only. This value can be positive, negative or zero Example.
REVIEW OVER VECTORS I. Scalars & Vectors: A scalar is a quantity that is defined by its value only. This value can be positive, negative or zero Example mass = 5 kg A vector is a quantity that can be described
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1  LOADING SYSTEMS
EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1  LOADING SYSTEMS TUTORIAL 1 NONCONCURRENT COPLANAR FORCE SYSTEMS 1. Be able to determine the effects
More informationLab 1: Units and Conversions
Lab 1: Units and Conversions The Metric System In order to measure the properties of matter, it is necessary to have a measuring system and within that system, it is necessary to define some standard dimensions,
More informationPHYS 1111L LAB 2. The Force Table
In this laboratory we will investigate the vector nature of forces. Specifically, we need to answer this question: What happens when two or more forces are exerted on the same object? For instance, in
More informationUnits of Measurement and Dimensional Analysis
POGIL ACTIVITY.2 POGIL ACTIVITY 2 Units of Measurement and Dimensional Analysis A. Units of Measurement The SI System and Metric System T here are myriad units for measurement. For example, length is
More informationA Mathematical Toolkit. Introduction: Chapter 2. Objectives
A Mathematical Toolkit 1 About Science Mathematics The Language of Science When the ideas of science are epressed in mathematical terms, they are unambiguous. The equations of science provide compact epressions
More informationCork Institute of Technology. CIT Mathematics Examination, Paper 1 Sample Paper A
Cork Institute of Technology CIT Mathematics Examination, 2015 Paper 1 Sample Paper A Answer ALL FIVE questions. Each question is worth 20 marks. Total marks available: 100 marks. The standard Formulae
More informationELEMENTS OF VECTOR ALGEBRA
ELEMENTS OF VECTOR ALGEBRA A.1. VECTORS AND SCALAR QUANTITIES We have now proposed sets of basic dimensions and secondary dimensions to describe certain aspects of nature, but more than just dimensions
More informationy = a sin ωt or y = a cos ωt then the object is said to be in simple harmonic motion. In this case, Amplitude = a (maximum displacement)
5.5 Modelling Harmonic Motion Periodic behaviour happens a lot in nature. Examples of things that oscillate periodically are daytime temperature, the position of a weight on a spring, and tide level. If
More information