Announcements LAST chance to do Math Skills test is Friday (1/29) at 4:30 pm in HL G59. No class after 5pm Thursday April 1. Instead of Lab that week, Statistics Quiz. Can be taken during any scheduled lab time except after 5pm Thursday. Reminder do Pre-Lab for lab 1 Before Lab. If late to Lab (by more than 10 min) you are considered absent. Mastering Physics assignment due Saturday (1/30), next due Monday (2/1). Bring your “Student Workbook” and Homework notebook to your discussion section. Tuesdays at 4:30 pm in G59, Review the current materials using MCAT Questions.

Inclined Plane   g g Sin(  ) We effectively have a way adjust the value of g.

General Relations Near the earth’s surface Gravity is just a constant acceleration a=g=9.8m/s 2 Down (it is a vector).

Scalars, Vectors, Tensors Scalar (A measurable quantity describable by a singular number) –Temperature, length, speed, brightness, time, pressure, volume, area, energy,…. Vector (A measurable quantity describable by a one or more numbers including a direction of some sort). –Position, velocity, acceleration, force, momentum, color, a row or column of numbers, electric field, magnetic field, some sets of functions, …. Tensor (More complicated mathematical structure). –Matrix, spinners, ….

Vectors Vectors are things which obey the algebra of vectors. (a lot of help) A Vector must have a magnitude and a direction. Vectors Commute Vector AdditionVector Scalar (dot) product Vectors Distributive Magnitude of a Vector

Vector times a scalar Some Vector examples

More on Vectors scalar product  Vector Scalar (dot) product Vectors Distributive

Unit Vectors A vector whose magnitude =1. Orthogonal unit vectors

Completing the Algebra Vector, Cross,Product Does not commute Will better define and use later

Examples of Vector Addition

What Happens to our Equations? Assuming k is up ^

One Effect We Treat the motion in each direction independently.

Coordinate Systems No Physics should depend on/require a Coordinate system. A coordinate system is an artificial grid like construct which we mental impose over our surroundings. We can place the “Origin” any place we feel like. We can rotate it to point the axis in any direction we like.

Good properties We like axis which are perpendicular to each other. We like right handed coordinate system. We have already used coordinate system in Lab and when plotting graphs. i k ^ ^ j ^ j ^ i ^

Some Coordinate Systems we have already used Km m   g g Sin(  )

Force Vector Rotated Coordinates   W=900N WxWx º FfFf If the box does not fall down, then the sum of the forces in i direction must be zero.  ^  

More Examples

Example of Dot Product