Chapter 3 Vectors 3 Chapter 3 Vector Quantities

Chapter 3 Vectors 第 3章 向量

Chapter 3 Vector Quantities 3 -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

3 -1 What is Physics? • Size • Direction

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

Displacement vector

3 -3 Adding Vectors Geometrically • Vector sum 向量和 (resultant 合量)

commutative law 交換律 associative law 結合律

commutative law

associative law

Sample Problem

3 -4 Components of Vectors • A component (分量) of a vector is the projection of the vector on an axis

Resolving the vector 向量分解

Vector Notation 向量記號 • component notation • magnitude-angle notation

Sample Problem

Trigonometric function 對邊 鄰邊 • hypotenuse 斜邊 • degree 度 • radian 弧度、弳、弳度 (rad)

Inverse trigonometric functions 反三角函數 • = sin 1 • = cos 1 • = tan 1

3 -5 Unit Vectors 單位向量 • right-handed coordinate system 右手坐標系

3 -6 Adding Vectors by Components

Sample Problem

Sample Problem

3 -7 Vectors and the Laws of Physics

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),

Scalar Product

Vector Product

Vector Product

Vector Product