Mathematics Algebra. It is used to describe the world around us.
|
|
- Meredith Powell
- 5 years ago
- Views:
Transcription
1 is a language. It is used to describe the world around us. Can you tell me what this means? N i I i1 If you understand only how to do the math, you will need to know the numbers to see any meaning behind this equation. However, if you understand the meaning of the math, the equation itself tells you a great deal about how nature works. The equation says the following 1 The total torque acting on an object is the same as its moment of inertia multiplied by its angular acceleration. is a language. N i I i1 means that The total torque acting on an object is the same as its moment of inertia multiplied by its angular acceleration. You see i is any of N torques, I is moment of inertia and is angular acceleration. N means to sum all of what is behind it for every value of i from 1 to N. i1 2 But you still do not know the meaning of torque, moment of inertia and angular acceleration. 1
2 is a language. N i I i1 means that The total torque acting on an object is the same as its moment of inertia multiplied by its angular acceleration. But you still do not know the meaning of torque, moment of inertia and angular acceleration. Torque is a measure of how hard you are trying turn something. Moment of inertia tells us how hard it is to change how fast it turns. And angular acceleration measures how much it changes how fast it turns. 3 is a language. N i I i1 means that The total torque acting on an object is the same as its moment of inertia multiplied by its angular acceleration. Torque is a measure of how hard you are trying turn something. Moment of inertia tells us how hard it is to change how fast it turns. And angular acceleration measures how much it changes how fast it turns. This same equation can describe a grinding wheel, the hands of a clock, the motion of a wrench, and an infinite number of other situations. 4 If I plug in the numbers as an example, I only learn ONE of the situations!! 2
3 You need to remember algebra. Here are some of the basics If A B C A B B C B A C B If A B C A B / B C / B A C / B Distributive property A B C A B AC Commutative properties A B B A A B B A and similarly for square roots, squares, subtraction and division except that subtraction and division are NOT commutative! 5 Some simple examples If F F ma 1x 2x x F F ma 1x 2x x Distributive property m v v mv mv 1x 2x 1x 2x If ma z F TOTALz m F / a TOTALz z Commutative properties m1 m2 m2 m1 ma x a m x and similarly for square roots, squares, subtraction and division except that subtraction and division are NOT commutative! 6 m1 m2 m2 m1 m/ a a / m x x 3
4 Here are some other helpful concepts If and A C B C A B Ratios If and AC D BC E 7 even if YOU DON T KNOW C! Simultaneous Equations + a Ab B c a Ab B c da a A db b B dc c usually we use this in such a way that one of the coefficients is zero A D B E even if YOU DON T KNOW C! Here are some more simple examples 8 If and F 1x 1 F F ma ma 2x 1 F 1x 2x even if YOU DON T KNOW m or a 1! Simultaneous Equations + 2F 6Q 10 12F 5Q F6 6 5Q usually we use this in such a way that one of the coefficients is zero Ratios If m1l T1 and m L K m m 2 2 T K even if YOU DON T KNOW L! 0F35Q57 57 Q 35 4
5 Finding out which equation or set of equations to use while solving a problem in physics is the most difficult part of the process. It is also the most crucial part! Still, if you follow a few basic steps, the difficulty will be far less and you will need to spend much less time on PreAssignments, Homework and Exams. An example solved by a naïve student (Bailey D. Wonderdog s nemesis, the neighbors cat, for instance) will help us see what the rules are and how to apply them. 9 If you look in your textbook, you will find the equation IR At first this naively appears to be the simplest equation we can use for this problem. We might be tempted to guess that is the velocity, I is the impulse, and R is the radius. 10 Let s try this 5
6 IR When trying to plug in the numbers, we see our first challenge. There two different objects and each have different velocities. 11 Which one do we choose? To answer this, we must ask ourselves two things. 1. What physical quantity are we looking for? 2. What object is that physical variable related to? For this problem, the answers are 1. Impulse 2. The ball IR Thus, we would use the quantities associated with the ball in this problem. 12 Rule #1: We must know which object we are considering in a problem. 10 Plugging in the numbers, we see that I 0.5. R 20 If we plug this into the homework software, it will tell us we are incorrect. What went wrong. 6
7 IR Well, first of all, the velocity is in m/s and the radius is in cm. So, we have to convert one of the units to make them the same. You will learn how to do this in the lecture called Math for Physics. If we do it properly in this case, we find that 13 m 10 s 100 cm I 50 s R 20 cm 1 m Rule #2: Use the proper units. 1 IR Next we go back to the very first thing we learned in this lecture. The variables of physics are words in the language of math. If we look up the equation again and read carefully, we will find that it means 14 The voltage across a resistive element in a circuit is the same as the current through it multiplied by its resistance. The variables are not even close to what we wanted to use!!!! 7
8 Rule #3: Know the IR meaning of each variable. We now look up the word impulse in the index of our book or in the notes and find that the variable that represents it is J. We now find two equations that contain J on the website for the class. J Favg t and J mv 15 But which one should we use? Rule #4: Use what is known and unknown to sort out equations J mv that are not useful. is the only one of the two equations for which we have all of the information to solve. It reads The impulse on an object is the same as its mass multiplied by the change in its velocity. We know the mass and the change in the velocity of the ball. 16 The other equation needed force and time, neither of which is known. 8
9 J mv Now we just need to plug in the ball s mass (40 g) and its change in velocity. It had 10 m/s to begin with and ended with 10 m/s as well. Thus, J mv 10 g 0 m / s 0 g m / s 17 But the homework software stills says that we are incorrect! 18 J mv The arrows on top of the variables J and v tell us that they are vectors. When we subtract the initial from the final velocity, we must also take into account their direction. (One is north, the other south). Rule #5: ectors! Gotta use vectors!!! J mv 10 g 10 m / s 10 m / s 20 g m / s Which is the correct answer!!!!!!!! 9
10 In summary... Rule #1: We must know which object we are considering in a problem. Rule #2: Use the proper units. Rule #3: Know the meaning of each variable. Rule #4: Use what is known and unknown to sort out equations that are not useful. Rule #5: ectors! Gotta use vectors!!! Follow these rules when solving problems and you will find that physics is not so bad. 19 This is what DR. Mike means when he says you must use concepts to solve problems in physics. 10
Math Lecture 3 Notes
Math 1010 - Lecture 3 Notes Dylan Zwick Fall 2009 1 Operations with Real Numbers In our last lecture we covered some basic operations with real numbers like addition, subtraction and multiplication. This
More informationA. Incorrect! Check your algebra when you solved for volume. B. Incorrect! Check your algebra when you solved for volume.
AP Chemistry - Problem Drill 03: Basic Math for Chemistry No. 1 of 10 1. Unlike math problems, chemistry calculations have two key elements to consider in any number units and significant figures. Solve
More informationMath 5a Reading Assignments for Sections
Math 5a Reading Assignments for Sections 4.1 4.5 Due Dates for Reading Assignments Note: There will be a very short online reading quiz (WebWork) on each reading assignment due one hour before class on
More informationA. Incorrect! Perform inverse operations to find the solution. B. Correct! Add 1 to both sides of the equation then divide by 2 to get x = 5.
Test-Prep Math - Problem Drill 07: The Multi-Step Equations Question No. 1 of 10 1. Solve: 2x 1 = 9 Question #01 (A) 4 (B) 5 (C) 1/5 (D) -5 (E) 0 B. Correct! Add 1 to both sides of the equation then divide
More informationDEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS LSN 8-8: ANGULAR MOMENTUM AND ITS CONSERVATION Questions From Reading Activity? Big Idea(s): The interactions of an object with other objects can be
More informationPhysics 1301, Exam 3 Review
c V Andersen, 2006 1 Physics 1301, Exam 3 Review The following is a list of things you should definitely know for the exam, however, the list is not exhaustive. You are responsible for all the material
More informationDEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS LSN 8-7: ROTATIONAL KINETIC ENERGY Questions From Reading Activity? Big Idea(s): The interactions of an object with other objects can be described by
More informationAlgebra Year 10. Language
Algebra Year 10 Introduction In Algebra we do Maths with numbers, but some of those numbers are not known. They are represented with letters, and called unknowns, variables or, most formally, literals.
More informationThe trick is to multiply the numerator and denominator of the big fraction by the least common denominator of every little fraction.
Complex Fractions A complex fraction is an expression that features fractions within fractions. To simplify complex fractions, we only need to master one very simple method. Simplify 7 6 +3 8 4 3 4 The
More information2x + 5 = x = x = 4
98 CHAPTER 3 Algebra Textbook Reference Section 5.1 3.3 LINEAR EQUATIONS AND INEQUALITIES Student CD Section.5 CLAST OBJECTIVES Solve linear equations and inequalities Solve a system of two linear equations
More informationACTIVITY 3. Learning Targets: 38 Unit 1 Equations and Inequalities. Solving Inequalities. continued. My Notes
Learning Targets: Write inequalities to represent real-world situations. Solve multi-step inequalities. SUGGESTED LEARNING STRATEGIES: Create Representations, Guess and Check, Look for a Pattern, Think-Pair-Share,
More informationMath101, Sections 2 and 3, Spring 2008 Review Sheet for Exam #2:
Math101, Sections 2 and 3, Spring 2008 Review Sheet for Exam #2: 03 17 08 3 All about lines 3.1 The Rectangular Coordinate System Know how to plot points in the rectangular coordinate system. Know the
More informationLinear Algebra. Introduction. Marek Petrik 3/23/2017. Many slides adapted from Linear Algebra Lectures by Martin Scharlemann
Linear Algebra Introduction Marek Petrik 3/23/2017 Many slides adapted from Linear Algebra Lectures by Martin Scharlemann Midterm Results Highest score on the non-r part: 67 / 77 Score scaling: Additive
More informationRotation of Rigid Objects
Notes 12 Rotation and Extended Objects Page 1 Rotation of Rigid Objects Real objects have "extent". The mass is spread out over discrete or continuous positions. THERE IS A DISTRIBUTION OF MASS TO "AN
More informationLecture 3i Complex Systems of Equations (pages )
Lecture 3i Complex Systems of Equations (pages 47-48) Now that we have covered the fundamentals of the complex numbers, we want to move on to study the vector space properties of the complex numbers. As
More information5.1 Simplifying Rational Expressions
5. Simplifying Rational Expressions Now that we have mastered the process of factoring, in this chapter, we will have to use a great deal of the factoring concepts that we just learned. We begin with the
More informationA. Incorrect! Replacing is not a method for solving systems of equations.
ACT Math and Science - Problem Drill 20: Systems of Equations No. 1 of 10 1. What methods were presented to solve systems of equations? (A) Graphing, replacing, and substitution. (B) Solving, replacing,
More informationSome Review Problems for Exam 1: Solutions
Math 3355 Fall 2018 Some Review Problems for Exam 1: Solutions Here is my quick review of proof techniques. I will focus exclusively on propositions of the form p q, or more properly, x P (x) Q(x) or x
More informationPhysics 1A Lecture 10B
Physics 1A Lecture 10B "Sometimes the world puts a spin on life. When our equilibrium returns to us, we understand more because we've seen the whole picture. --Davis Barton Cross Products Another way to
More informationMath Review for Chemistry
Chemistry Summer Assignment 2018-2019 Chemistry Students A successful year in Chemistry requires that students begin with a basic set of skills and knowledge that you will use the entire year. The summer
More informationChapter 1 Review of Equations and Inequalities
Chapter 1 Review of Equations and Inequalities Part I Review of Basic Equations Recall that an equation is an expression with an equal sign in the middle. Also recall that, if a question asks you to solve
More informationRotation of Rigid Objects
Notes 12 Rotation and Extended Objects Page 1 Rotation of Rigid Objects Real objects have "extent". The mass is spread out over discrete or continuous positions. THERE IS A DISTRIBUTION OF MASS TO "AN
More informationModesto Junior College Course Outline of Record PHYS 101
Modesto Junior College Course Outline of Record PHYS 101 I. OVERVIEW The following information will appear in the 2011-2012 catalog PHYS 101 General Physics: Mechanics 5 Units Prerequisite: Satisfactory
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department 8.01 Physics I Fall Term 2009 Review Module on Solving N equations in N unknowns
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department 8.01 Physics I Fall Term 2009 Review Module on Solving N equations in N unknowns Most students first exposure to solving N linear equations in N
More informationBefore this course is over we will see the need to split up a fraction in a couple of ways, one using multiplication and the other using addition.
CH MORE FRACTIONS Introduction I n this chapter we tie up some loose ends. First, we split a single fraction into two fractions, followed by performing our standard math operations on positive and negative
More informationAlgebra Year 9. Language
Algebra Year 9 Introduction In Algebra we do Maths with numbers, but some of those numbers are not known. They are represented with letters, and called unknowns, variables or, most formally, literals.
More informationAstronomy 102 Math Review
Astronomy 102 Math Review 2003-August-06 Prof. Robert Knop r.knop@vanderbilt.edu) For Astronomy 102, you will not need to do any math beyond the high-school alegbra that is part of the admissions requirements
More informationMath 90 Lecture Notes Chapter 1
Math 90 Lecture Notes Chapter 1 Section 1.1: Introduction to Algebra This textbook stresses Problem Solving! Solving problems is one of the main goals of mathematics. Think of mathematics as a language,
More informationInduction and Inductance
Welcome Back to Physics 1308 Induction and Inductance Michael Faraday 22 September 1791 25 August 1867 Announcements Assignments for Tuesday, November 6th: - Reading: Chapter 30.6-30.8 - Watch Videos:
More informationLECSS Physics 11 Introduction to Physics and Math Methods 1 Revised 8 September 2013 Don Bloomfield
LECSS Physics 11 Introduction to Physics and Math Methods 1 Physics 11 Introduction to Physics and Math Methods In this introduction, you will get a more in-depth overview of what Physics is, as well as
More informationUniversity of Colorado at Colorado Springs Math 090 Fundamentals of College Algebra
University of Colorado at Colorado Springs Math 090 Fundamentals of College Algebra Table of Contents Chapter The Algebra of Polynomials Chapter Factoring 7 Chapter 3 Fractions Chapter 4 Eponents and Radicals
More informationProperties of Arithmetic
Excerpt from "Prealgebra" 205 AoPS Inc. 4 6 7 4 5 8 22 23 5 7 0 Arithmetic is being able to count up to twenty without taking o your shoes. Mickey Mouse CHAPTER Properties of Arithmetic. Why Start with
More information1.4 Mathematical Equivalence
1.4 Mathematical Equivalence Introduction a motivating example sentences that always have the same truth values can be used interchangeably the implied domain of a sentence In this section, the idea of
More informationContents. Objectives Torque on an Object Rotational Kinetic Energy Yo yo Rolling on an Incline Physical Pendulum Angular Momentum and Torque Recap
Physics 121 for Majors Class 21 Rotating Objects Last Class We learned to find angular momentum and torques of point masses and objects. We learned how to use torques and forces to solve problems with
More informationSTANDARDS OF LEARNING CONTENT REVIEW NOTES. ALGEBRA I Part I. 2 nd Nine Weeks,
STANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA I Part I 2 nd Nine Weeks, 2016-2017 OVERVIEW Algebra I Content Review Notes are designed by the High School Mathematics Steering Committee as a resource
More informationHW9 Concepts. Alex Alemi November 1, 2009
HW9 Concepts Alex Alemi November 1, 2009 1 24.28 Capacitor Energy You are told to consider connecting a charged capacitor together with an uncharged one and told to compute (a) the original charge, (b)
More informationUnit 6 Study Guide: Equations. Section 6-1: One-Step Equations with Adding & Subtracting
Unit 6 Study Guide: Equations DUE DATE: A Day: Dec 18 th B Day: Dec 19 th Name Period Score / Section 6-1: One-Step Equations with Adding & Subtracting Textbook Reference: Page 437 Vocabulary: Equation
More informationReview for 3 rd Midterm
Review for 3 rd Midterm Midterm is on 4/19 at 7:30pm in the same rooms as before You are allowed one double sided sheet of paper with any handwritten notes you like. The moment-of-inertia about the center-of-mass
More informationHonors Advanced Mathematics Determinants page 1
Determinants page 1 Determinants For every square matrix A, there is a number called the determinant of the matrix, denoted as det(a) or A. Sometimes the bars are written just around the numbers of the
More informationLESSON #1: VARIABLES, TERMS, AND EXPRESSIONS COMMON CORE ALGEBRA II
1 LESSON #1: VARIABLES, TERMS, AND EXPRESSIONS COMMON CORE ALGEBRA II Mathematics has developed a language all to itself in order to clarify concepts and remove ambiguity from the analysis of problems.
More information2 Foundations of physics Calculation sheet. OCR Physics A. Determining uncertainty. Specification references. Learning outcomes
Determining uncertainty Specification references 2.2.1 c) M0.3 Use ratios, fractions, and percentages M1.5 Identify uncertainties in measurements and use simple techniques to determine uncertainty when
More informationVectors. Advanced Math Circle. October 18, 2018
Vectors Advanced Math Circle October 18, 2018 Today we are going to spend some time studying vectors. Vectors are not only ubiquitous in math, and also used a lot in physics and engineering. Vectors are
More informationMathematics E-15 Seminar on Limits Suggested Lesson Topics
Mathematics E-15 Seminar on Limits Suggested Lesson Topics Lesson Presentation Guidelines Each lesson should last approximately 45 minutes. This will leave us with some time at the end for constructive
More informationWe ll start today by learning how to change a repeating decimal into a fraction! Then we will do a review of Unit 1 - half of Unit 3!
Welcome to math! We ll start today by learning how to change a repeating decimal into a fraction! Then we will do a review of Unit 1 - half of Unit 3! So grab a seat where you can focus, and get ready
More informationExam 2 Solutions. x 1 x. x 4 The generating function for the problem is the fourth power of this, (1 x). 4
Math 5366 Fall 015 Exam Solutions 1. (0 points) Find the appropriate generating function (in closed form) for each of the following problems. Do not find the coefficient of x n. (a) In how many ways can
More informationFinding Limits Graphically and Numerically
Finding Limits Graphically and Numerically 1. Welcome to finding limits graphically and numerically. My name is Tuesday Johnson and I m a lecturer at the University of Texas El Paso. 2. With each lecture
More informationGUIDED NOTES 2.2 LINEAR EQUATIONS IN ONE VARIABLE
GUIDED NOTES 2.2 LINEAR EQUATIONS IN ONE VARIABLE LEARNING OBJECTIVES In this section, you will: Solve equations in one variable algebraically. Solve a rational equation. Find a linear equation. Given
More informationPhysics 12 Rules for Significant Digits and Rounding
1 Physics 12 Rules for Significant Digits and Rounding One mathematical aspect of problem-solving in the physical sciences that gives some students difficulty deals with the rounding of computed numerical
More informationSeries, Parallel, and other Resistance
EELE 2310 Analysis Lecture 3 Equivalent s Series, Parallel, Delta-to-Wye, Voltage Divider and Current Divider Rules Dr Hala El-Khozondar Series, Parallel, and other Resistance Equivalent s ١ Overview Series,
More informationPhysics 218 Lecture 21
Physics 218 Lecture 21 Dr. David Toback Physics 218, Lecture XXI 1 Checklist for Today Things due Yesterday Chapters 12 & 13 in WebCT Things that are due for today Read Chapters 14-16 Things that are due
More informationCLASS NOTES: BUSINESS CALCULUS
CLASS NOTES: BUSINESS CALCULUS These notes can be thought of as the logical skeleton of my lectures, although they will generally contain a fuller exposition of concepts but fewer examples than my lectures.
More informationMost people said that they understand force and acceleration. GOOD!
Questions and Answers on Dynamics 3/17/98 Thanks to the students who submitted questions and comments! I have grouped them by topic and shortened some of the long questions/comments. Please feel free to
More informationMITOCW 2. Harmonic Oscillators with Damping
MITOCW 2. Harmonic Oscillators with Damping The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources
More informationBasic Math Problems Unit 1
Basic Math Problems Unit 1 Name Period Using fractions: When you are using fractions in science, we need to convert them into decimals. You can do this by dividing the top number by the bottom number.
More informationMITOCW MITRES18_005S10_DiffEqnsMotion_300k_512kb-mp4
MITOCW MITRES18_005S10_DiffEqnsMotion_300k_512kb-mp4 PROFESSOR: OK, this lecture, this day, is differential equations day. I just feel even though these are not on the BC exams, that we've got everything
More informationPlease bring the task to your first physics lesson and hand it to the teacher.
Pre-enrolment task for 2014 entry Physics Why do I need to complete a pre-enrolment task? This bridging pack serves a number of purposes. It gives you practice in some of the important skills you will
More informationAP Physics 1 Summer 2016 Assignment
Quakertown Community High School AP Physics 1 Summer 2016 Assignment The AP Physics 1 course focuses on the big ideas typically included in the first semester of an algebra-based, introductory college-level
More informationPhysics 8 Friday, October 20, 2017
Physics 8 Friday, October 20, 2017 HW06 is due Monday (instead of today), since we still have some rotation ideas to cover in class. Pick up the HW07 handout (due next Friday). It is mainly rotation, plus
More informationAn Introduction to Proofs in Mathematics
An Introduction to Proofs in Mathematics The subject of mathematics is often regarded as a pinnacle in the achievement of human reasoning. The reason that mathematics is so highly regarded in the realm
More informationCherry Creek High School Summer Assignment for students entering: Accelerated CP Geometry
Cherry Creek High School Summer Assignment for students entering: Accelerated CP Geometry Please have the following worksheets completed and ready to be handed in on the first day of class in the fall.
More information(arrows denote positive direction)
12 Chapter 12 12.1 3-dimensional Coordinate System The 3-dimensional coordinate system we use are coordinates on R 3. The coordinate is presented as a triple of numbers: (a,b,c). In the Cartesian coordinate
More informationPhysics 218 Lecture 23
Physics 218 Lecture 23 Dr. David Toback Physics 218, Lecture XXIII 1 Checklist for Today Things due Monday Chapter 14 in WebCT Things that were due yesterday Chapter 15 problems as Recitation Prep Things
More informationMATH 320, WEEK 6: Linear Systems, Gaussian Elimination, Coefficient Matrices
MATH 320, WEEK 6: Linear Systems, Gaussian Elimination, Coefficient Matrices We will now switch gears and focus on a branch of mathematics known as linear algebra. There are a few notes worth making before
More informationBefore this course is over we will see the need to split up a fraction in a couple of ways, one using multiplication and the other using addition.
CH 0 MORE FRACTIONS Introduction I n this chapter we tie up some loose ends. First, we split a single fraction into two fractions, followed by performing our standard math operations on positive and negative
More informationA summary of factoring methods
Roberto s Notes on Prerequisites for Calculus Chapter 1: Algebra Section 1 A summary of factoring methods What you need to know already: Basic algebra notation and facts. What you can learn here: What
More informationRotation and Angles. By torque and energy
Rotation and Angles By torque and energy CPR An experiment - and things always go wrong when you try experiments the first time. (I won t tell you the horror stories of when I first used clickers, Wattle
More informationNote that we are looking at the true mean, μ, not y. The problem for us is that we need to find the endpoints of our interval (a, b).
Confidence Intervals 1) What are confidence intervals? Simply, an interval for which we have a certain confidence. For example, we are 90% certain that an interval contains the true value of something
More informationSolve Systems of Equations Algebraically
Part 1: Introduction Solve Systems of Equations Algebraically Develop Skills and Strategies CCSS 8.EE.C.8b You know that solutions to systems of linear equations can be shown in graphs. Now you will learn
More informationPrecalculus Chapter P.1 Part 2 of 3. Mr. Chapman Manchester High School
Precalculus Chapter P.1 Part of 3 Mr. Chapman Manchester High School Algebraic Expressions Evaluating Algebraic Expressions Using the Basic Rules and Properties of Algebra Definition of an Algebraic Expression:
More information2 Analogies between addition and multiplication
Problem Analysis The problem Start out with 99% water. Some of the water evaporates, end up with 98% water. How much of the water evaporates? Guesses Solution: Guesses: Not %. 2%. 5%. Not 00%. 3%..0%..5%.
More informationName Date Time to Complete
Name Date Time to Complete h m Partner Course/ Section / Grade Complex Circuits In this laboratory you will connect electric lamps together in a variety of circuits. The purpose of these exercises is to
More informationUpon successful completion of this course, students should be competent to perform the following tasks:
Course Information Course Prefix/Number: PHY 221 Course Title: University Physics Lecture Hours/Week: 3.0 Lab Hours/Week: 3.0 Credit Hours/Semester: 4.0 VA Statement/Distance Learning Attendance Textbook
More informationCourse Project. Physics I with Lab
COURSE OBJECTIVES 1. Explain the fundamental laws of physics in both written and equation form 2. Describe the principles of motion, force, and energy 3. Predict the motion and behavior of objects based
More informationTake the Anxiety Out of Word Problems
Take the Anxiety Out of Word Problems I find that students fear any problem that has words in it. This does not have to be the case. In this chapter, we will practice a strategy for approaching word problems
More informationNumbers. The aim of this lesson is to enable you to: describe and use the number system. use positive and negative numbers
Module One: Lesson One Aims The aim of this lesson is to enable you to: describe and use the number system use positive and negative numbers work with squares and square roots use the sign rule master
More informationConceptual Explanations: Simultaneous Equations Distance, rate, and time
Conceptual Explanations: Simultaneous Equations Distance, rate, and time If you travel 30 miles per hour for 4 hours, how far do you go? A little common sense will tell you that the answer is 120 miles.
More informationImportant. Need a more in depth preview? Get ALL the premium chapter 1 tutorials FREE
MATH1505.com We Make Math Easy. PREVIEW Homework ~ Tutorials ~ Past Tests Important Math 1505 is a HUGE course. Many students fear the course, but you don t need to, you ve got us! Your keys to success
More informationPhysics 8 Friday, November 4, 2011
Physics 8 Friday, November 4, 2011 Please turn in Homework 7. I will hand out solutions once everyone is here. The handout also includes HW8 and a page or two of updates to the equation sheet needed to
More informationA-2. Polynomials and Factoring. Section A-2 1
A- Polynomials and Factoring Section A- 1 What you ll learn about Adding, Subtracting, and Multiplying Polynomials Special Products Factoring Polynomials Using Special Products Factoring Trinomials Factoring
More informationCHAPTER 7: TECHNIQUES OF INTEGRATION
CHAPTER 7: TECHNIQUES OF INTEGRATION DAVID GLICKENSTEIN. Introduction This semester we will be looking deep into the recesses of calculus. Some of the main topics will be: Integration: we will learn how
More information1. The first thing you need to find is the mass of piece three. In order to find it you need to realize that the masses of the three pieces must be
1. The first thing you need to find is the mass of piece three. In order to find it you need to realize that the masses of the three pieces must be equal to the initial mass of the starting rocket. Now
More informationLecture 10: Powers of Matrices, Difference Equations
Lecture 10: Powers of Matrices, Difference Equations Difference Equations A difference equation, also sometimes called a recurrence equation is an equation that defines a sequence recursively, i.e. each
More informationMath 2142 Homework 5 Part 1 Solutions
Math 2142 Homework 5 Part 1 Solutions Problem 1. For the following homogeneous second order differential equations, give the general solution and the particular solution satisfying the given initial conditions.
More informationElectric Circuits Part 2: Kirchhoff s Rules
Electric Circuits Part 2: Kirchhoff s Rules Last modified: 31/07/2018 Contents Links Complex Circuits Applying Kirchhoff s Rules Example Circuit Labelling the currents Kirchhoff s First Rule Meaning Kirchhoff
More informationInverse Kinematics. Mike Bailey. Oregon State University. Inverse Kinematics
Inverse Kinematics Mike Bailey mjb@cs.oregonstate.edu inversekinematics.pptx Inverse Kinematics Forward Kinematics solves the problem if I know the link transformation parameters, where are the links?.
More informationEGN 3310 Practice Final Spring 2017
EGN 3310 Practice Final Spring 2017 *Try finishing each problem in 15 minutes or less to practice test-like time contraints. The topics on the practice exam are what I feel have been stressed in class,
More informationAP Physics 1 Summer Assignment #
APPhysics1 SummerAssignment AP Physics 1 Summer Assignment Welcome to AP Physics 1. This course and the AP exam will be challenging. AP classes are taught as college courses not just college-level courses,
More informationProblem Solving. Undergraduate Physics
in Undergraduate Physics In this brief chapter, we will learn (or possibly review) several techniques for successful problem solving in undergraduate physics courses Slide 1 Procedure for The following
More informationMath 1320, Section 10 Quiz IV Solutions 20 Points
Math 1320, Section 10 Quiz IV Solutions 20 Points Please answer each question. To receive full credit you must show all work and give answers in simplest form. Cell phones and graphing calculators are
More informationIntroduction to Algebra: The First Week
Introduction to Algebra: The First Week Background: According to the thermostat on the wall, the temperature in the classroom right now is 72 degrees Fahrenheit. I want to write to my friend in Europe,
More informationMath 308 Midterm Answers and Comments July 18, Part A. Short answer questions
Math 308 Midterm Answers and Comments July 18, 2011 Part A. Short answer questions (1) Compute the determinant of the matrix a 3 3 1 1 2. 1 a 3 The determinant is 2a 2 12. Comments: Everyone seemed to
More informationHow to write maths (well)
How to write maths (well) Dr Euan Spence 29 September 2017 These are the slides from a talk I gave to the new first-year students at Bath, annotated with some of the things I said (which appear in boxes
More informationChapter 2. Polynomial and Rational Functions. 2.5 Zeros of Polynomial Functions
Chapter 2 Polynomial and Rational Functions 2.5 Zeros of Polynomial Functions 1 / 33 23 Chapter 2 Homework 2.5 p335 6, 8, 10, 12, 16, 20, 24, 28, 32, 34, 38, 42, 46, 50, 52 2 / 33 23 3 / 33 23 Objectives:
More informationChapter 3 ALGEBRA. Overview. Algebra. 3.1 Linear Equations and Applications 3.2 More Linear Equations 3.3 Equations with Exponents. Section 3.
4 Chapter 3 ALGEBRA Overview Algebra 3.1 Linear Equations and Applications 3.2 More Linear Equations 3.3 Equations with Exponents 5 LinearEquations 3+ what = 7? If you have come through arithmetic, the
More informationSystem of Linear Equation: with more than Two Equations and more than Two Unknowns
System of Linear Equation: with more than Two Equations and more than Two Unknowns Michigan Department of Education Standards for High School: Standard 1: Solve linear equations and inequalities including
More informationAP Physics C Syllabus
Course Overview AP Physics C Syllabus AP Physics C will meet for 90 minutes on block scheduling and for 45 minutes on regular scheduling. Class activities will include lecture, demonstration, problem solving
More informationLesson 21 Not So Dramatic Quadratics
STUDENT MANUAL ALGEBRA II / LESSON 21 Lesson 21 Not So Dramatic Quadratics Quadratic equations are probably one of the most popular types of equations that you ll see in algebra. A quadratic equation has
More informationPHYS 185 Final Exam December 4, 2012
PHYS 185 Final Exam December 4, 2012 Name: Answer the questions in the spaces provided on the question sheets. If you run out of room for an answer, continue on the back of the page. Please make an effort
More information8.012 Physics I: Classical Mechanics Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 8.012 Physics I: Classical Mechanics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. MASSACHUSETTS INSTITUTE
More informationReview of Circuit Analysis
Review of Circuit Analysis Fundamental elements Wire Resistor Voltage Source Current Source Kirchhoff s Voltage and Current Laws Resistors in Series Voltage Division EE 42 Lecture 2 1 Voltage and Current
More information