Physics notes.


This, my friends, is a semester long experiment. For the entire semester, I will posting all of my Physics 140 for the University of Michigan notes online.

Keep in mind, this is none of the homework, none of anything except my notes while reading through the text.

CHAPTER 1 – Units, Physical Quantities, and Vectors

  1. Vectors are used to describe and analyze physical quantities, such as velocity and force, that have direction as well as magnitude.
  2. Physics = experiment science
  3. Theory = explanation of natural phenomena based on observation and accepted fundamental principles.
  4. physics is a process
  5. Range of validity
  6. physics process- identify relevant concepts, set up problem, execute the solution, evaluate
  7. model -simplified version of a physical system
  8. good models = simplify a problem enough to make it manageable, yet keeps essential features
  9. operational definition = some physcial quantities that are so fundamental we can only define them by describing how to measure them.
  10. unit = standard to compare to
  11. cesium atom correlation to second
  12. newton = SI unit of force
  13. uncertainty = distinction between different measurement
  14. accuracty = how close to the true value
  15. fractional error/percent error = percentwise how off your value was from true


  • Scalars are just size (magnitude)
  • combining scalars is just simple addition
  • combining vectors involves taking both direction and magnitude into consideration
  • head to tail method: extremely useful, but less accurate
  • add the negative of a vector to subtract
  • odd thing: two huge vectors added may be 0
  • |A| = magnitude of a vector
  • Q: Magnitude of A + B is greater than or equal to |A-B|
  • |A-B| is smallest when they are in the same direction
  • more precise methods of adding vectors involves using x, y axises
  • |Vx| = |V|cosø  (x component)
  • |Vy| = |V|sinø (ycomponent)
  • Unit vector = vector with unit of 1
  • unit vector î = x direction
  • unit vector ˆj  = y direction
  • unit vector ˆk = z direction
  • A = Axî + Ay ˆj + Azˆk
  • Multiplication of Vectors
  • multiply by scalar
  • dot product and cross product
  • matrix multiplication
  • not possible to divide vectors
  • |c|A = cA
  • Scalar Product = dot product
  • A•B=|C|
  • A•B=|A||B|cosø
  • This essentially finds the amount of one vector that points in the direction of the other vector
  • Tells how parallel the two vectors are
  • Cross method needs to be discussed more….


  • Overall we are discussing motion in one dimension first
  • THIS is much easier since we can express vectors in one dimension as a signed number
  • + = right, – = left  (or up/down)
  • Displacement = distance an object has moved from its starting position
  • it is a vector that points from a starting point to an end point
  • ∆S = Sf – Si
  • Velocity is simply displacement over time
  • Speed is the magnitude of the velocity vector
  • Instantaneous velocity = V instant = lim (∆t=>0) (∆s/∆t) = ds/dt
  • Be sure to examine the relationship between s, v, a
  • NOTE: when you take the integral you have no idea what the starting position was or ending position was, you just know the slope of the graph
  • Without air resistance, all objects regardless of their mass will fall at the same rate.
  • Demoed in class
  • Air friction complicates the speed of falling objects

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