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    ViOLET Chào mừng năm học mới

    English for physics

    Nhấn vào đây để tải về
    Báo tài liệu có sai sót
    Nhắn tin cho tác giả
    (Tài liệu chưa được thẩm định)
    Nguồn:
    Người gửi: Nguyễn Thị Kim Anh
    Ngày gửi: 10h:19' 18-08-2017
    Dung lượng: 2.6 MB
    Số lượt tải: 2
    Số lượt thích: 0 người
    UNIT 1: VECTOR
    English for Physics
    GROUP EP150-4R
    VECTOR
    EP150-4R
    Velocity?
    Work?
    Energy?
    Mass?
    A study of motion involves the introduction of various quantities that are used to describe the physical world. Examples of such quantities include distance, displacement, speed, velocity, acceleration, force, mass, momentum, energy, work, power, etc….
    All of these quantities can be divided into two categories: vectors and scalars.
    A vector quantity is fully described by its magnitude and direction.
    In contrast, a scalar quantity is fully described by its magnitude
    The emphasis of this lecture is to understand some fundamental properties of vectors and to apply these properties in order to understand motion and forces that occur in two dimensions.

    VECTORS
    READING
    SCALARS
    EP150-4R
    VECTOR
    Basic concepts of vector
    1
    Basic vector operations
    2
    The dot product of two vectors
    3
    Cross product of two vectors
    4
    EP150-4R
    VECTOR
    The scalar triple product of three vectors
    5
    BASIC CONCEPT OF VECTOR
    EP150-4R
     
    Graphical of a vector
     
    BASIC CONCEPT OF VECTOR
    A unit vector
    EP150-4R
     
    BASIC CONCEPT OF VECTOR
    EP150-4R
    c) Parallel vectors
    Two vectors (which may have different magnitudes) are said to be parallel if they are parallel to the same line.
    If two vectors point toward opposite direction, they are called anti-parallel vector.
    In summary, two vectors are parallel if one vector is a scalar multiples of other.
    BASIC CONCEPT OF VECTOR
    EP150-4R
    d) Equal vectors
    The length or magnitude of a vector is the distance between the initial and terminal points of the vector. The length of a vector AB is denoted by , so
    If two vectors a and b have the same length and direction, they are said to be equal and denoted by
    The vector that has the same magnitude as but points toward opposite direction is called the opposite vector of and denoted by . Each vector has a unique opposite vector.
    BASIC CONCEPT OF VECTOR
    EP150-4R
     
    BASIC CONCEPT OF VECTOR
    EP150-4R
    Negation vector
    a) Sum of two vectors (Vector addition)



    BASIC VECTOR OPERATIONS
    EP150-4R
    The sum of two vectors
     
    BASIC VECTOR OPERATIONS
    EP150-4R
    BASIC VECTOR OPERATIONS
    a) Sum of two vectors (Vector addition)
    EP150-4R
    The triangle rule
    The parallelogram rule
    BASIC VECTOR OPERATIONS
    a) Sum of two vectors (Vector addition)
    EP150-4R
     
    Commutation:
    Associative:
    Adding with a zero vector:
     
    BASIC VECTOR OPERATIONS
    EP150-4R
    Distributive
    Associative
    Associative
    Associative
    c) Scalar multiple of a vector
    BASIC VECTOR OPERATIONS
    EP150-4R
    Definition:
    Given two non-zero vectors and , the dot product of two vectors and , denoted by , is a scalar defined by the formula: , where is the angle between and
    For example, in physics, we know that if a force acts on an object and moves it a distance s, then the work A of the force is calculated by the formula:
    THE DOT PRODUCT OF TWO VECTORS
    EP150-4R
    THE DOT PRODUCT OF TWO VECTORS
    EP150-4R
    Properties
    Commutation:
    Distributive:
    Scalar Mutiplication:
    Definition:
    Given two non-zero vectors and , the cross product of two vectors and , denoted by , is the vector defined by the formula: , where is the angle between and ; is a unit vector perpendicular plane of vector and
    The choice between two (opposite) directions that are perpendicular to both and is determined by the right hand rude.

    CROSS PRODUCT OF TWO VECTORS
    EP150-4R
    The right – hand rule
    Properties
    CROSS PRODUCT OF TWO VECTORS
    EP150-4R
    Definition:
    The scalar triple product (also called the mixed product, box product or triple scalar product) is defined as the dot product of one of the vectors with the cross product of the other two:

    THE SCALAR TRIPLE PRODUCT OF TREE VECTORS
    EP150-4R
    Three vectors defining a parallelepiped
    Definition:
    In Cartesian coordinate, we have:
    THE SCALAR TRIPLE PRODUCT OF TREE VECTORS
    EP150-4R
    Properties
    Circular shift
    THE SCALAR TRIPLE PRODUCT OF TREE VECTORS
    EP150-4R
    Negates
    Properties
    The scalar triple product can also be understood as the determinant of the 3×3 matrix (thus also its inverse) having the three vectors either as its rows or its columns (a matrix has the same determinant as its transpose):

    THE SCALAR TRIPLE PRODUCT OF TREE VECTORS
    EP150-4R
    EP150-4R
     
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