Recap of 1-D Kinematics - McMaster University

Recap of 1-D Kinematics - McMaster University

Vectors Scalars and Vectors Vector Components and Arithmetic Vectors in 3 Dimensions Unit vectors i, j, k Serway and Jewett Chapter 3 Physics 1D03 - Lecture 3 1 Physical quantities are classified as scalars, vectors, etc. Scalar : described by a real number with units examples: mass, charge, energy . . . Vector : described by a scalar (its magnitude) and a direction in space

examples: displacement, velocity, force . . . Vectors have direction, and obey different rules of arithmetic. Physics 1D03 - Lecture 3 2 Notation Scalars : ordinary or italic font (m, q, t . . .) Vectors : - Boldface font (v, a, F . . .) - arrow notation ( v, a, F . . .) - underline (v, a, F . . .)

Pay attention to notation : constant v and constant v mean different things! Physics 1D03 - Lecture 3 3 Magnitude : a scalar, is the length of a vector. e.g., Speed, v = |v| (a scalar), is the magnitude of velocity v Multiplication: A scalar vector = vector 3 A 2

12 A Later in the course, we will use two other types of multiplication: the dot product , and the cross product. Physics 1D03 - Lecture 3 4 Vector Addition: Vector + Vector = Vector A e.g. A B C Triangle Method A

B C A B B Parallelogram Method A C A B B Physics 1D03 - Lecture 3 5 Concept Quiz Two students are moving a refrigerator. One pushes with a force of 200 newtons, the other with a

force of 300 newtons. Force is a vector. The total force they (together) exert on the refrigerator is: a) equal to 500 newtons b) equal to 200 2 300 2 newtons c) not enough information to tell Physics 1D03 - Lecture 3 6 Concept Quiz Two students are moving a refrigerator. One pushes with a force of 200 newtons (in the positive direction), the other with a force of 300 newtons in the opposite direction. What is the net force ? A) 100 N B) -100 N C) 500 N

Physics 1D03 - Lecture 3 7 Coordinate Systems In 2-D : describe a location in a plane y by polar coordinates : (x,y) distance r and angle r y by Cartesian coordinates : 0 x

x distances x, y, parallel to axes with: x=rcos y=rsin Physics 1D03 - Lecture 3 8 Components define the axes first y v x , v y , (and v z ) are scalars axes dont have to be horizontal and vertical v vy vx

x the vector and its components form a right triangle with the vector on the hypotenuse Physics 1D03 - Lecture 3 9 Magnitude : the length of a vector. Magnitude is a scalar. e.g., Speed is the magnitude of velocity: velocity = v ; speed = |v| = v In terms of components: y | v | v x2 v y2 On the diagram, vx = v cos

v vy vx x vy = v sin Physics 1D03 - Lecture 3 10 3-D Coordinates (location in space) We use a right-handed coordinate system with three axes: z y y x

x z Physics 1D03 - Lecture 3 11 x Is this a right-handed coordinate system? Does it matter? y z Physics 1D03 - Lecture 3 12 Unit Vectors

A unit vector u or u is a vector with magnitude 1 : u 1 z (a pure number, no units) k Define coordinate unit vectors i, j, k along the x, y, z axis. j y i x Physics 1D03 - Lecture 3 13

A vector A can be written in terms of its components: A Ax i Ay j Az k A Ay j A Ay j j i Ax i Ax i

Physics 1D03 - Lecture 3 14 Addition again: If A + B = C , A Ay Ax B By Bx then: Cx Ax Bx Cy Ay By

Tail to Head Cz Az Bz Three scalar equations from one vector equation! B C A Ax By Cy Bx Ay

Cx Physics 1D03 - Lecture 3 15 The unit-vector notation leads to a simple rule for the components of a vector sum: A B C In components (2-D for simplicity) : A B ( Ax Bx ) i ( Ay By ) j Cx i Cy j Eg: A=2i+4j B=3i-5j A+B = 5i-j A - B = -i+9j Physics 1D03 - Lecture 3 16 Summary vector quantities must be treated according to the

rules of vector arithmetic vectors add by the triangle rule or parallelogram rule (geometric method) a vector A can be represented in terms of its Cartesian components using the unit vectors i, j, k these can be used to add vectors (algebraic method) C A B if and only if: Cx Ax Bx Cy Ay By Cz Az Bz Physics 1D03 - Lecture 3 17

Recently Viewed Presentations

  • Internet Computing and the Emerging Grid

    Internet Computing and the Emerging Grid

    Conclusions The HPC will be dominated by Peer-to-Peer Grid of clusters. Adaptive, scalable, and easy to use Systems and End-User applications will be prominent. Access electricity, internet, entertainment (music, movie,…), etc. from the wall socket! An Economics -based Service Oriented...
  • Module 1

    Module 1

    Difficulty with reading comprehension or math skills. Trouble with open-ended test questions and word problems. Dislikes reading and writing; avoids reading aloud. Spells the same word differently in a single document. Poor organizational skills (desk is messy and disorganized) Trouble...
  • International Institute of Christian Discipleship PEv 05 Reaching

    International Institute of Christian Discipleship PEv 05 Reaching

    Historicism- Prophetic interpretation. Purpose and timing of the judgment. Confusion with Mormons and Jehovah's Witnesses . Mostly due to . ... The easiest way is to use the Old Testament prophecies about the first coming of Jesus. Then show the...
  • Steric hindrance at the electrophilic carbon slows the

    Steric hindrance at the electrophilic carbon slows the

    Steric hindrance at the electrophilic carbon slows the SN2 reaction. no SN2 polar solvents especially good for SN1 (OK for some SN2) aprotic solvents (no H on O or N) cannot H-bond to Nu especially good for SN2 Intramolecular Reactions...
  • Fulton County Board of Health - Atlanta City Council

    Fulton County Board of Health - Atlanta City Council

    Access to services offered through FCBOH Neighborhood Union and in Grady Partnership at Asa G. Yancey Health Center. Strategic public health partner within the Morehouse School of Medicine Department of Community Health's cluster in the HUD funded place-based initiative to...
  • Veterans Benefits Administration NCD Programs Overview & Best

    Veterans Benefits Administration NCD Programs Overview & Best

    Provide the last date credit accrued in the "LD Accrued" box. Process a Pro Rata refund. Any debt with VA will be on the student. If the student is allowed to return after termination (AVOID this scenario when possible): Contact...
  • Question Bank 1- English IV  Which intellectual and

    Question Bank 1- English IV Which intellectual and

    Wordsworth believed that poetry should express… The spontaneous overflow of power emotions. An objective truth about observed reality. Concepts of superficial beauty, not necessarily with deeper meaning. The collective "will" of the people.
  • CME Guides - University of Florida

    CME Guides - University of Florida

    Applicants and licensed drivers who have a chronic recurring seizure disorder (or who have been treated for such for 1 year) and medications have been discontinued will not be licensed to drive during the period of drug withdrawal and for...