Tìm kiếm theo tiêu đề

Tìm kiếm Google

Quảng cáo

Quảng cáo

Quảng cáo

Hướng dẫn sử dụng thư viện

Hỗ trợ kĩ thuật

Liên hệ quảng cáo

  • (04) 66 745 632
  • 0166 286 0000
  • contact@bachkim.vn

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: 4
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
 
Gửi ý kiến