Lecture 3
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Velocity is a vector !
Vectors
Free Fall again
Intro to the Motions in Two
and Three Dimensions
http://web.njit.edu/~sirenko/
Velocity has direction !
Velocity can change with time
Physics 105, Fall 2009
Lecture 3
Andrei Sirenko, NJIT
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Andrei Sirenko, NJIT
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Writing Vectors
Chapter 3: Vectors
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Lecture 3
Vectors and Scalars
Adding Vectors Geometrically
Components of Vectors
Unit Vectors
Adding Vectors by Components
Vectors and the Laws of Physics
Multiplying Vectors
We need to distinguish vectors
From other quantities (scalars)
Common notation:
Bold face: c or Arrow:
c
– Scalar Product
– Vector or Cross Product
Lecture 3
Andrei Sirenko, NJIT
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Lecture 3
Andrei Sirenko, NJIT
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Vectors and Scalars
Displacement
Lecture 3
Components of Vectors:
Path length and Displacement
Andrei Sirenko, NJIT
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Trig Review
Length (Magnitude)
Lecture 3
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Unit Vectors and Coordinate Systems
2D (2 dimensions)
3D (3 dimensions)
Lecture 3
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Lecture 3
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Lecture 3
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Lecture 3
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Laws of Vector Addition
Lecture 3
Andrei Sirenko, NJIT
Last Lecture:
Vector Multiplication
Motion along the straight line + Vectors
Scalar product
Three dimension (2D)
One dimension (1D)
Position:
Velocity:
Acceleration:
x(t) m
v(t) m/s
a(t) m/s2
All are vectors: have direction and
magnitude.
Position:
r(t) m
Velocity:
v(t) m/s
Acceleration: a(t) m/s2
X=0
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Lecture 3
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Relative Motion/Reference Frames
Lecture 3
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Lecture 3
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Relative Motion/Reference Frames
Lecture 3
Andrei Sirenko, NJIT
Relative Motion/Reference Frames
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Lecture QZ3
A=(4m)·i + (2m)·j and
B = (–1m)·i + (2m)·j
1.
What is the length (or magnitude) of the vector C if C=A+B
⏐C⏐=???
2.
What is the angle between vectors A and B
θ=???
3.
What is the scalar (dot) product of the same vectors A and B:
(A·B)=???
A
B
4. (huge extra credit) What is the magnitude of the vector (cross)
product of the same vectors A and B:
⏐A×B⏐=???
Hint: i and j are the unit vectors.
Lecture 3
Andrei Sirenko, NJIT
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Lecture 3
Andrei Sirenko, NJIT
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