chapter 3: two dimensional...
TRANSCRIPT
Copyright © 2010 Pearson Education, Inc.
Chapter 3: Two Dimensional
Kinematics
3.1. Vectors in Physics
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Q: The1-D Equations of Motion from the
last chapter are OK; but how do we
describe motion in the real 3-D world?
A: With 2-D and 3-D vectors.
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Scalars and Vectors
• A scalar is a single numerical value (e.g.
mass, distance, speed) and has magnitude.
• A vector has magnitude (i.e. length) and
direction.
In two dimensions, if
you only know that the
library is 0.5 miles
away, you do not know
its position unless you
also know its direction.
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Representing Vectors
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Components of Vectors
To resolve a vector means to find its components.
Its components are the lengths of the vector along
specified (orthogonal, i.e. perpendicular) directions.
To say the library
is 4.24 blocks to
the northwest is
the same as to
say it is 3 blocks
north and 3
blocks west.
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Trigonometry in 5 Minutes
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Trigonometry in 5 Minutes
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Computing Vector Components
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Example 1
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Angle is counterclockwise from the X axis
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However in word
problems, watch
out if alternative
angles are given.
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From Components to Vectors
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Example 2
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Example 3
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Warning
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A certain vector has x and y components
that are equal in magnitude. Which of the
following is a possible angle for this vector
in a standard x-y coordinate system?
1) 30°
2) 180°
3) 90°
4) 60°
5) 45°
ConcepTest 3.2b Vector Components II
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A certain vector has x and y components
that are equal in magnitude. Which of the
following is a possible angle for this vector
in a standard x-y coordinate system?
1) 30°
2) 180°
3) 90°
4) 60°
5) 45°
The angle of the vector is given by tan q = y/x. Thus, tan q = 1
in this case if x and y are equal, which means that the angle
must be 45°.
ConcepTest 3.2b Vector Components II
Or 135º, 225º or 315º!
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Motion in Three Dimensions