1 / 17

Vectors

Vectors. Scalars and Vectors Vector Components and Arithmetic Vectors in 3 Dimensions Unit vectors i , j , k. Serway and Jewett Chapter 3. Physical quantities are classified as scalars, vectors, etc. Scalar : described by a real number with units

tovi
Télécharger la présentation

Vectors

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 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

  2. 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

  3. Notation • Scalars : ordinary or italic font (m, q, t . . .) • Vectors : - Boldface font (v, a, F . . .) - arrow notation - underline (v, a, F . . .) • Pay attention to notation : “constant v” and “constant v” mean different things! Physics 1D03 - Lecture 3

  4. Magnitude : a scalar, is the “length” of a vector. e.g., Speed, v = |v| (a scalar), is the magnitude of velocity v Multiplication: scalar  vector = vector Later in the course, we will use two other types of multiplication: the “dot product” , and the “cross product”. Physics 1D03 - Lecture 3

  5. Vector Addition: Vector + Vector = Vector Parallelogram Method Triangle Method Physics 1D03 - Lecture 3

  6. 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: • equal to 500 newtons • equal to newtons • not enough information to tell Physics 1D03 - Lecture 3

  7. 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)100Nb)-100Nc) 500N Physics 1D03 - Lecture 3

  8. Coordinate Systems In 2-D : describe a location in a plane y • by polar coordinates : • distance r and angle  • by Cartesian coordinates : • distances x, y, parallel to axes with: x=rcosθ y=rsinθ ( x , y ) r y  x 0 x Physics 1D03 - Lecture 3

  9. y vy vx x Components • define the axes first • are scalars • axes don’t have to be horizontal and vertical • the vector and its components form a right triangle with the vector on the hypotenuse Physics 1D03 - Lecture 3

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

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

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

  13. Ayj Ayj j i Axi Axi A vector can be written in terms of its components: Physics 1D03 - Lecture 3

  14. By Ay Ax Bx By Cy Bx Ay Ax Cx Addition again: IfA + B = C , then: Tail to Head Three scalar equations from one vector equation! Physics 1D03 - Lecture 3

  15. The unit-vector notation leads to a simple rule for the components of a vector sum: In components (2-D for simplicity) : Eg: A=2i+4j B=3i-5j A+B = 5i-j A - B = -i+9j Physics 1D03 - Lecture 3

  16. y vy  vx x 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: On the diagram, vx = v cos vy = v sin Physics 1D03 - Lecture 3

  17. 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 can be represented in terms of its Cartesian components using the “unit vectors” i, j, kthese can be used to add vectors (algebraic method) • if and only if: Physics 1D03 - Lecture 3

More Related