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TRANSCRIPT
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Martha Casquete
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Read Chapter 3 (Vectors) HW3 Set due next Tuesday, 9/17 Pg. 68 – 70: 1, 4, 11, 16, 26, 32, 43 (8th edition)
Question/Observation Thursdays
Research Q/O Tuesdays with HW (due date
Tuesdays)
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Coordinate Systems
Vector and Scalar Quantities
Properties of Vectors
Component of Vector and Unit Vectors
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Distance and displacement
Average velocity and average speed
Instantaneous velocity and speed
Acceleration
Free fall acceleration:
a = g =- 9.80 m/s2
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Would you risk your life driving drunk?
Intro
2
002
1gttvxx
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In 2-D : describe a location in a plane
• by polar coordinates : distance r and angle • by Cartesian coordinates :
distances x, y, parallel to axes
with: x = rcosθ y = rsinθ x
y
r
( x , y )
0 x
y
• Since we know the Cartesian coordinates, we can find r and :
• x
ytan
22 yxr
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A fly lands on one wall of a room. The lower left corner of the wall is selected as the origin of a two-dimensional Cartesian coordinate system. If the fly is located at the point having coordinates (2.00, 1.00) m , (a) how far is it from origin? (b) What is its location in polar coordinates?
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Physical quantities are classified as scalars, vectors, etc.
Scalar : described by a real number with units
examples: mass, charge, energy . . .
Vector : described by a scalar (its magnitude) and a direction in space
examples: displacement, velocity, force . . .
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Vectors have direction, and obey different rules of arithmetic.
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Scalars : ordinary or italic font (m, q, t . . .) Vectors : - Boldface font (v, a, F . . .) - arrow notation
Pay attention to notation :
“constant v” and “constant v” mean different things!
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.) . . F ,a ,v(
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Magnitude : a scalar, is the “length” of a vector.
e.g., Speed, v = |v| (a scalar), is the magnitude of velocity v
3.3 Properties of Vectors
Direction
Commutative Law Associative Law of addition
ABBA
CBACBA
)()(
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CBA
e.g.
A B
Triangle Method Parallelogram Method
A
B
A
B
BAC
BAC
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CBA
e.g.
A
B
A
B
BAC
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Two students are moving a refrigerator. One pushes with a force of 200 newtons, the other with a force of 300 newtons. Force is a vector. The total force they (together) exert on the refrigerator is:
a) equal to 500 newtons b) equal to newtons c) not enough information to tell
22 300200
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Two students are moving a refrigerator. One pushes with a force of 200 newtons (in the positive direction), the other with a force of 300 newtons in the opposite direction. What is the net force ?
a)100N
b)-100N
c) 500N
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A A
2
3
A
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Multiplication: scalar vector = vector
Later in the course, we will use two other types of multiplication: the “dot product” , and the “cross product”.
Follow the steps for Example 2.3 from your book (pg. 60)
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define the axes first
are scalars
axes don’t have to be horizontal and vertical
the vector and its components form a right triangle with the vector on the hypotenuse
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) (and , , zyx vvv
x
y
vy
vx
v
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cos vvx
x
y
vy
vx
v
yv
sin vvy
xv
22
yx vvv
x
y
v
v1tan
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Choose the correct response to make the sentence true: A component is
(a) always
(b) never
( c ) sometimes
…..larger than the magnitude of the vector.
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---Specify a given direction Define coordinate unit vectors i, j, k along the x, y, z axis.
z
y
x
i
j
k
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A vector can be written in terms of its components: A
kAjAiAA zyx
i
j
A
Ax i
Ay j
Ay j
Ax i
A
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Ax
Ay A
By
Bx
B
By
Bx
B
Ay
Ax
A
C
Cx
Cy
If A + B = C , then:
zzz
yyy
xxx
BAC
BAC
BAC
Three scalar equations from one vector equation!
Tail to Head
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BA
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CBA
In components (2-D for simplicity) :
jiji )( )( yxyyxx CCBABA
The unit-vector notation leads to a simple rule for the components of a vector sum:
Eg: A=2i+4j B=3i-5j
A+B = 5i-j A - B = -i+9j
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Magnitude : the “length” of a vector. Magnitude is a scalar.
In terms of components: On the diagram, vx = v cos vy = v sin
x
y
vy
vx
v
e.g., Speed is the magnitude of velocity: velocity = v ; speed = |v| = v
22|| yx vv v
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Example 2
While exploring a cave, a spelunker starts at the entrance and moves the following distances in a horizontal plane. She goes 75.0 m north, 250 m east, 125m at an angle θ = 30˚ north of east, and 150 m south. Find her resultant displacement from the cave entrance.
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vector quantities must be treated according to the rules of vector arithmetic
vectors add by the triangle rule or parallelogram rule (geometric method)
a vector can be represented in terms of its Cartesian components using the “unit vectors” i, j, k these can be used to add vectors (algebraic method)
if and only if:
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A
BAC
zzzyyyxxx BACBACBAC