The Week 4 Physics Reading Assignment is Ch. 3.1, 3.2, and 3.4.
- Since we’re not reading Ch. 3.3 yet, those of you who haven’t studied trigonometry before might be confused about the references to sin, cos, tan, etc. We’ll return to these soon, but for now all you need to know is that if you know an angle associated with a vector (in this case, the velocity vector), the trigonometric functions are used to calculate the x-component and the y-component of the velocity. Or, if you know the x-component and y-component of a vector, you can use the inverse trigonometric functions to determine the angle of the vector.
- Ch. 3.2 is included in this reading to give us an introduction to some of the concepts and terminology involved with vectors and especially components of vectors. Key ideas include: that a vector has a direction and magnitude; that kinematics quantities like displacement, velocity, and acceleration are vector quantities; how vectors are represented symbolically and graphically (pictorially); how to draw, add and subtract, and stretch/compress vectors graphically; how to resolve a vector into its components graphically. We’ll return to Ch. 3.2 in a few weeks when we study vectors in more detail during our study of trigonometry, at which point we will also look at Ch. 3.3 and learn analytical techniques to supplement our graphical approach.
- Once we have the idea that a velocity vector can be broken up into its x-component and y-component, we can address the main physics idea of this reading: the Independence of Perpendicular Motions. Look closely at that discussion in Ch. 3.1, and pay particular attention to Figure 3.6 and Figure 3.38.
- It’s easy to get overwhelmed by thinking there are a lot of formulas. Once you get past that initial response (take deep breaths), note that the motion in the x-direction is described by a constant velocity model and its associated equations (eqs. (3.33), (3.34), (3.35)), and that the motion in the y-direction is described by a constant (free-fall) acceleration model and its associated equations (eqs. (3.36), (3.38), (3.39), and (3.40)) Oh – plus the Pythogorean theorem. The key equations are (3.33) thru (3.40).
- Examples 3.4 and 3.5 are a good place to concentrate your attention after your initial read. Please review 1. above for notes about the use of the trigonometric and inverse trigonometric functions: they are used to break the initial velocity vector into its x-component and y-component or to take the components to determine the direction of the vector. At this point, we will only deal with velocities that have already been decomposed into horizontal and vertical components and won’t ask for directions given components.