Phys141 Class Notes: Vectors and Two-Dimensional Motion - Prof. Wolfgang Losert, Study notes of Physics

These class notes cover the topics of vectors, two-dimensional motion, and related concepts such as adding and subtracting vectors, multiplying or dividing a vector by a scalar, and motion in two dimensions. The notes also include information on position and displacement vectors, velocity vectors, and acceleration. From a physics 141 class and includes equations and diagrams.

Typology: Study notes

Pre 2010

Uploaded on 02/13/2009

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Phys141 – Mon 9/11
Today:
Rest of Chapter 3: Vectors
Chapter 4.1: Two dimensional motion
For Wed:
Read Chapters 4.4 and 4.5 (you can skip 4.6)
Online Quiz
Prepare the pre-lab 1-2 paragraph writeup
that has to be handed in prior to lab.
Note on Lab: Normal distribution
Example: Spheres randomly going left or right
as they fall down. After about 10 left-right
decisions, on average the sphere will be in
the center, but it may also be a bit to the
left or to the right.
Now, if 100 spheres are dropped, we can
predict how many will end up straight down,
and how many will end up one right, two
right, one left etc.
Statistics: Can predict what happens on average, and what
the probabilities are for a single sphere, even though we
can’t predict what exactly a single sphere will do!
Vertical direction: y
Gravitational acceleration: g= 9.8 m/s2
Objects starts at position yiwith velocity vi
At time t, it is at positon y(t)
Equation for falling object
2
1
() 2
ii
yt y vt gt=+ +
Chapter 2
pf3
pf4
pf5

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Download Phys141 Class Notes: Vectors and Two-Dimensional Motion - Prof. Wolfgang Losert and more Study notes Physics in PDF only on Docsity!

Phys141 – Mon 9/

Today:

  • Rest of Chapter 3: Vectors
  • Chapter 4.1: Two dimensional motion

For Wed:

  • Read Chapters 4.4 and 4.5 (you can skip 4.6)
  • Online Quiz
  • Prepare the pre-lab 1-2 paragraph writeup that has to be handed in prior to lab.

Note on Lab: Normal distribution

Example: Spheres randomly going left or right as they fall down. After about 10 left-right decisions, on average the sphere will be in the center, but it may also be a bit to the left or to the right. Now, if 100 spheres are dropped, we can predict how many will end up straight down, and how many will end up one right, two right, one left etc.

Statistics: Can predict what happens on average, and what the probabilities are for a single sphere, even though we can’t predict what exactly a single sphere will do!

Vertical direction: y

Gravitational acceleration: g = 9.8 m/s 2

Objects starts at position y (^) i with velocity v (^) i

At time t , it is at positon y(t)

Equation for falling object

y t = y i + v ti + g t

Chapter 2

Motion in 2D

Note: this is x-y graph, not x-time graph!

First – define vectors…

x-y graph

Chapter 3+

Chapter 3: Vectors

  • Mathematical tool to describe motion in one, two and three dimensions
  • Vector has
    • magnitude
    • Direction
  • Scalar has only magnitude
  • Graphical: Vectors generally drawn as arrows
  • In one dimension:

Example: velocity

Example: speed

Chapter 3

2D: Magnitude and direction of vector A

Magnitude r

Direction: θ generally counter clockwise from positive x axis

tan θ =

y

x

A

Chapter 3

r = x^2 + y^2

Subtracting Vectors

  • Special case of vector addition
  • AB , same as A +( -B )
  • Continue with standard vector addition procedure

Chapter 3

Multiplying or Dividing a Vector by a Scalar

  • Result is a vector

Magnitude: Original vector magnitude multiplied or divided by the scalar

Direction: Positive scalar – same as original direction Negative scalar – opposite direction as original

Chapter 3

Motion in 2D:

Position and Displacement vectors

Position vector r relative to origin

Displacement: change in position Δ r = r f – r i

Question: Assuming the particle moves at constant speed, plot x vs time x-y graph

Chapter 4

Motion in 2D:

Velocity vectors

Instantaneous velocity v

  • direction of v : along tangent to path of the particle
  • Magnitude of v: speed (one cannot tell speed from x-y graph!!!)

0

lim

t

d

Δ → t^ dt

r r

v

trajectory

Chapter 4

Acceleration

  • The instantaneous acceleration is the

limit of the average acceleration as

Δ v /Δ t approaches zero

  • For constant acceleration:

0

lim

t

d

Δ → t^ dt

v v

a

x t = x i + v i t + a t

Chapter 4

To Do

  • Read Chapters 4.4 and 4.5 (you can skip 4.6)

and do pre-class quiz

  • Homework due Friday