1 / 26

Physics 114A - Mechanics Lecture 5 (Walker: 3.1-3) Vectors January 13, 2014

Physics 114A - Mechanics Lecture 5 (Walker: 3.1-3) Vectors January 13, 2014. John G. Cramer Professor Emeritus, Department of Physics B451 PAB jcramer@uw.edu. Announcements.

ace
Download Presentation

Physics 114A - Mechanics Lecture 5 (Walker: 3.1-3) Vectors January 13, 2014

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. Physics 114A - MechanicsLecture 5 (Walker: 3.1-3)VectorsJanuary 13, 2014 John G. Cramer Professor Emeritus, Department of Physics B451 PAB jcramer@uw.edu

  2. Announcements • Homework Assignments #1-3 are now available on WebAssign. Assignment #1 is due at 11:59 PM on Thursday, January 16. Be sure to do the “A” homework (not “B”). So far 194/219 students have registered for 114A on WebAssign. Everyone MUST register on WebAssign before Exam 1. • I will be flying to Arizona tonight, and tomorrow’s lecture will be given by Dr. Svetlana Gladycheva, who teaches Physics 114B. • Obtain a H-iTT clicker from the University Bookstore and register it (160/219), using the link on the Syllabus page. • If you are disabled and plan to take the 114A exams at the DRS Office in Mary Gates Hall, see Susan Miller as soon as possible to make arrangements. • The 117 labs start today. By 8:00 AM on the day of your lab, you must have completed the Pre-Lab exam on WebAssign. Physics 114A - Lecture 5

  3. Lecture Schedule (Part 1) We are here. Physics 114A - Lecture 5

  4. Scalars Versus Vectors Scalar: quantity is a number with units Vector: quantity has both a magnitude (with units) and a direction How to get to the Library: you need to know how far (0.5 miles) and which way. Physics 114A - Lecture 5

  5. The Components of a Vector Even though you know how far and in which direction the library is, you may not be able to walk there in a straight line: Physics 114A - Lecture 5

  6. 2D Cartesian and PolarCoordinate Representations Physics 114A - Lecture 5

  7. The Components of a Vector Length, angle, and components can be calculated from each other using trigonometry: Convention:We measure qcounterclockwisefrom the +x axis Physics 114A - Lecture 5

  8. Polar Coordinates Cartesian Coordinates The Components of a Vector We can resolve vector into perpendicular components using two-dimensional coordinate systems: Physics 114A - Lecture 5

  9. The Components of a Vector Signs of vector components and range of q: 180° £ q £ 270° 0 £ q £ 90° 90° £ q £ 180° 270° £ q £ 360° 4th quadrant 3rd quadrant 2nd quadrant 1st quadrant Physics 114A - Lecture 5

  10. Example: Height of a Cliff In Jules Vern’s Mysterious Island,Capt. Cyrus Harding wants to find theheight of a cliff. He stands with hisback to the base of the cliff andmarches straight away from it for 500 ft.At this point, he lies on the ground andmeasures the angle from horizontal tothe top of the cliff. (a) If the angle is 34.0°, how high is the cliff? (b) What is the straight line distance d from Capt. Harding to the top of the cliff? Physics 114A - Lecture 5

  11. Clicker Question 1 A vector has a negative x-component and a positive y-component. The angle q that specifies its direction is measured counterclockwise from the x axis. Then in what range is q ? Physics 114A - Lecture 5

  12. Adding Vectors Graphically Adding vectors graphically: Place the tail of the second at the head of the first. The sum points from the tail of the first to the head of the last. Physics 114A - Lecture 5

  13. Combining Vectors Graphically Physics 114A - Lecture 5

  14. Adding Vectors Physics 114A - Lecture 5

  15. Adding Vectors by Components • Adding Vectors Using Components: • Find the components of each vector to be added. • Add the x- and y-components separately. • Find the resultant vector. Physics 114A - Lecture 5

  16. Adding Vectors by Components Physics 114A - Lecture 5

  17. Subtracting Vectors Subtracting Vectors: The negative of a vector is a vector of the same magnitude pointing in the opposite direction. Here, D = A – B. Physics 114A - Lecture 5

  18. Subtracting Vectors Physics 114A - Lecture 5

  19. Multiplication by a Scalar Physics 114A - Lecture 5

  20. Properties of Vectors Physics 114A - Lecture 5

  21. Properties of Vectors Vectors are equal if they have the same magnitude and direction. Physics 114A - Lecture 5

  22. Vector Summary • Scalar: number, with appropriate units • Vector: quantity with magnitude and direction • Vector components:Ax = A cos θ, By = B sin θ • Magnitude:A = (Ax2 + Ay2)1/2 • Direction:θ= tan-1 (Ay / Ax) • Graphical vector addition: Place tail of second at head of first; sum points from tail of first to head of last Physics 114A - Lecture 5

  23. A·B is the magnitude of B times the projection of A on B (or vice versa). Note that A·B = B·A Multiplying Vectors* Given two vectors: Dot Product (Scalar Product) Example: work Cross Product (Vector Product)Example: torque (determinant) Physics 114A - Lecture 5

  24. Az R q Ay y Ax f 0 £ q £ p 0 £ f £ 2p x 3D Spherical Coordinates* z Spherical:One length + two angles. • Ax= R Sin q Cos f • Ay= R Sin q Sin f • Az= R Cos q • R = [Ax2 + Ay2 + Az2]½ = |A| • = Tan-1{[Ax2 + Ay2]½/Az} f = Tan-1[Ay/Ax] Physics 114A - Lecture 5

  25. z Az z Ay y Ax q r 0 £ q £ 2p x 3D Cylindrical Coordinates* Cylindrical:Two lengths + one angle • Ax= r Cos q • Ay= r Sin q • Az= z • r = [Ax2 + Ay2]½ • = Tan-1[Ay/Ax] z = Az Physics 114A - Lecture 5

  26. Before Tuesday, read Walker, Chapter 3.4-3.5 • Homework Assignments #1-3 are now available on WebAssign. Assignment #1 is due at 11:59 PM on Thursday, January 16. Be sure to do the “A” homework (not “B”). So far 194/219 students have registered for 114A on WebAssign. Everyone MUST register on WebAssign before Exam 1. • The 117 labs start today. By 8:00 AM on the day of your lab, you must have completed the Pre-Lab exam on WebAssign. End of Lecture 5

More Related