Text Reading: Giancoli, Physics - Principles with Applications, Chapter 3: Sections 1-4
- Section 1: To work with quantities like displacement, velocity, and acceleration that have both a size or magnitude (scalar value) and a direction, we need to use vectors.
- Section 2: Because vectors have direction as well as length, we have to take into account how the directions of vectors are related when we combine them. We can add vectors graphically, by putting the tail of each subsequent vector at the tip of the preceding vector, drawing a result vector from the tail of our first vector to the tip of our last vector.
- Section 3: We substract vectors graphically by reversing the direction of our second vector (the vector being subtracted). Multiplying vectors by scalars is really just scaling the vector; we don't change its direction.
- Section 4: To work with vectors mathematically, we have to add, subtract, or multiply the sections of the vectors that lie in a common direction. To do this, we break vectors down into components that match the directions in our frame of reference (usually an x-y coordinate system). The actual vector is assumed to be the result of adding an x-direction and y-direction vector together.
Resultant Vector Displacement (Vector Form from Component Vectors)
Resultant Vector Magnitude from Component Vectors
Resultant Vector Direction from Component Vectors (θ measured counter-clockewise from x-coordinate.)
Read the following weblecture before chat: Kinematics in Two and Three Dimensions
The website below will either download a Java applet to your computer or run the applet in place, depending on how your browser is configured. You will need Java installed to run the applet locally on your computer.
The "vector addition" applet lets you play with different representations of vectors. Grab a vector arrow from the bucket, and drag it onto the graph area to experiment. The display bar will show you the magnitude of the resultant vector |R|, the angle with respect to the X axis θ, and the component vectors Rx and Ry.
- Place a vector with its tail at the origin, the manipulate the point of a very short vector (|R| < 5) to achieve angles of 45°, 135°, 225°, and 315°. What happens to the values of Rx and Ry? Are they always positive?
- Place two vectors so that the tail of vector one is at the origin, and the tip is at the tail of vector two. Click the "Show Sum" option and move the resultant vector so that its tail rests on the tail of vector one. What happens now as you move the tip of vector two?
- Use the Style options to display the X and Y components of the vectors in different combinations.
- Try to solve one of the vector addition homework problems in your text using the simulation.
Physics simulation Java Applets are the product of the PHET Interactive Simulations project at the University of Colorado, Boulder.
Chat Preparation Activities
- Forum question: The Moodle forum for the session will assign a specific study question for you to prepare for chat. You need to read this question and post your answer before chat starts for this session.
- Mastery Exercise: The Moodle Mastery exercise for the chapter will contain sections related to our chat topic. Try to complete these before the chat starts, so that you can ask questions.
- The chapter quiz is not yet due.
If you want lab credit for this course, you must complete at least 12 labs (honors course) or 18 labs (AP students). One or more lab exercises are posted for each chapter as part of the homework assignment. We will be reviewing lab work at regular intervals, so do not get behind!
© 2005 - 2018 This course is offered through Scholars Online, a non-profit organization supporting classical Christian education through online courses. Permission to copy course content (lessons and labs) for personal study is granted to students currently or formerly enrolled in the course through Scholars Online. Reproduction for any other purpose, without the express written consent of the author, is prohibited.