chapter 3 vectors 第 3 章 向量. chapter 3 vector quantities 3-1 what is physics? 3-2 vectors and...
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Chapter 3 Vectors第 3 章 向量
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Chapter 3 Vector Quantities3-1 What is Physics?
3-2 Vectors and Scalars
3-3 Adding Vectors Geometrically
3-4 Components of Vectors
3-5 Unit Vectors
3-6 Adding Vectors by Components
3-7 Vectors and the Laws of Physics
3-8 Multiplying Vectors
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3-1 What is Physics?
• Size
• Direction
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3-2 Vectors and Scalars向量與純量
• Vector– magnitude 量值– direction 方向
• Vector quantities– Displacement, velocity, and acceleration
• Scalar quantities– Temperature, pressure, energy, mass, and
time
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Displacement vector
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3-3 Adding Vectors Geometrically
• Vector sum 向量和 (resultant 合量 )
s a b
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s a b
a b b a
( ) ( )a b c a b c
( ) 0b b
( )d a b a b
commutative law交換律
associative law結合律
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commutative law
a b b a
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associative law
( ) ( )a b c a b c
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( ) 0b b
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( )d a b a b
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Sample Problem
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3-4 Components of Vectors
• A component ( 分量 ) of a vector is the projection of the vector on an axis
2 2
cos and sin
and tan
x y
yx y
x
a a a a
aa a a
a
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Resolving the vector 向量分解
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Vector Notation 向量記號• component notation
• magnitude-angle notation
2 2
cos and sin
and tan
x y
yx y
x
a a a a
aa a a
a
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Sample Problem
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Trigonometric function
• hypotenuse 斜邊• degree 度• radian 弧度、弳、弳度 (rad)
鄰邊
對邊
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Inverse trigonometric functions反三角函數
= sin1
= cos1
= tan1
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3-5 Unit Vectors 單位向量
• right-handed coordinate system 右手坐標系
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ˆ ˆ ˆ ˆi j i jx y x ya a a b b b
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3-6 Adding Vectors by Components
x x x
y y y
z z z
r a b
r a b
r a b
r a b
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Sample Problem
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Sample Problem
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3-7 Vectors and the Laws of Physics
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3-8 Multiplying Vectors
• Multiplying a Vector by a Scalar
• Multiplying a Vector by a Vector– scalar product ( 純量積 ), dot product ( 點積 ),
inner product ( 內積 )– vector product ( 向量積 ), cross product ( 叉積 ), outer product ( 外積 ),
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Scalar Product
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Vector Product
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Vector Product
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Vector Product