SCALARS

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SCALARS VECTORS
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SCALARS VECTORS Scalar describes the type of
thing that has only a magnitude and can be
represented by a number. Examples are
temperature, mass, time, the money in your bank
account 32F, 62 kg, 1134 AM, 8.32
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SCALARS VECTORS Scalar describes the type of
thing that has only a magnitude and can be
represented by a number. Examples are
temperature, mass, time, the money in your bank
account 32F, 62 kg, 1134 AM, 8.32
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88005403
SCALARS VECTORS Scalar describes the type of
thing that has only a magnitude and can be
represented by a number. Examples are
temperature, mass, time, the money in your bank
account 32F, 62 kg, 1134 AM, 8.32
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88005403
SCALARS VECTORS Scalar describes the type of
thing that has only a magnitude and can be
represented by a number. Examples are
temperature, mass, time, the money in your bank
account 32F, 62 kg, 1134 AM, 8.32
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SCALARS VECTORS Vector describes the type of
thing that has both a magnitude AND a direction.
Examples include
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SCALARS VECTORS Vector describes the type of
thing that has both a magnitude AND a direction.
Examples include displacement distance and
direction and velocity speed and direction. 2
miles NE, 55 mph going east
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SCALARS VECTORS Vector describes the type of
thing that has both a magnitude AND a direction.
Examples include displacement distance and
direction and velocity speed and direction. 2
miles NE, 55 mph going east
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SCALARS VECTORS Vector describes the type of
thing that has both a magnitude AND a direction.
Examples include displacement distance and
direction and velocity speed and direction. 2
miles NE, 55 mph going east
N
N
Displacement vector 2 miles NE
Velocity vector 55 mph Eastward
E
E
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We use arrows to give a geometric representation
of vectors a picture the length of a vector
indicates magnitude and the orientation shows
direction
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We use arrows to give a geometric representation
of vectors a picture the length of a vector
indicates magnitude and the orientation shows
directionyou need to indicate a length scale and
a direction scale, e.g.
A displacement vector 2.75 miles in the NE
direction.
N
1 inch 1 mile
E
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We use arrows to give a geometric representation
of vectors a picture the length of a vector
indicates magnitude and the orientation shows
directionyou need to indicate a length scale and
a direction scale, e.g.
A velocity vector 63 mph in the NE direction.
N
1 inch 25 mph
E
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We often need to specify direction in more
detailconsider an traffic engineer laying out a
future roadway. Doing this requires an angle and
a reference direction north, east, south, west.
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We often need to specify direction in more
detailconsider an traffic engineer laying out a
future roadway. Doing this requires an angle and
a reference direction north, east, south,
west. Example,
A displacement vector of magnitude 2.75 miles
40 north of East
E
1 inch 25 mph
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Vectors (whatever type of quantity they
represent) add differently from the way numbers
dothey have to since they must keep track of
magnitude AND direction. Lets say we want to
add two vectors A and B
B
A
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Vectors (whatever type of quantity they
represent) add differently from the way numbers
dothey have to since they must keep track of
magnitude AND direction. Lets say we want to
add two vectors A and B
B
A
Graphically, we add them by parallel
transporting them till they connect tip to tail.
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Vectors (whatever type of quantity they
represent) add differently from the way numbers
dothey have to since they must keep track of
magnitude AND direction. Lets say we want to
add two vectors A and B
B
A
A B
Then we draw the arrow from the tail of A to
the tip of B. This is the vector (A B).
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General properties of vectors (displacement,
velocity, acceleration) 1. Multiple a vector
A by a positive number c and the vectors
magnitude becomes cA
A
3A
½ A
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General properties of vectors (displacement,
velocity, acceleration) 1. Multiple a vector
A by a positive number c and the vectors
magnitude becomes cA
A
3A
Note All these have the same direction!
½ A
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2. If you multiply a vector by (-1) then the
vector reverses direction (but keeps the same
magnitude)
-2B
-B
B
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If A was the velocity vector 5 m/s east
N
E
5 m/s East
Then the velocity vector
5 m/s West
could be written as -A