Download presentation

Presentation is loading. Please wait.

Published byMercy Gaines Modified over 2 years ago

1
Physics 1D03 - Lecture 31 Vectors Scalars and Vectors Vector Components and Arithmetic Vectors in 3 Dimensions Unit vectors i, j, k Serway and Jewett Chapter 3

2
Physics 1D03 - Lecture 32 Physical quantities are classified as scalars, vectors, etc. Scalar : described by a real number with units examples: mass, charge, energy... Vector : described by a scalar (its magnitude) and a direction in space examples: displacement, velocity, force... Vectors have direction, and obey different rules of arithmetic.

3
Physics 1D03 - Lecture 33 Notation Scalars : ordinary or italic font (m, q, t...) Vectors : - Boldface font (v, a, F...) - arrow notation - underline (v, a, F...) Pay attention to notation : “constant v” and “constant v” mean different things!

4
Physics 1D03 - Lecture 34 Magnitude : a scalar, is the “length” of a vector. e.g., Speed, v = |v| (a scalar), is the magnitude of velocity v Multiplication: scalar vector = vector Later in the course, we will use two other types of multiplication: the “dot product”, and the “cross product”.

5
Physics 1D03 - Lecture 35 Vector Addition: Vector + Vector = Vector Triangle Method Parallelogram Method

6
Physics 1D03 - Lecture 36 Concept Quiz Two students are moving a refrigerator. One pushes with a force of 200 newtons, the other with a force of 300 newtons. Force is a vector. The total force they (together) exert on the refrigerator is: a)equal to 500 newtons b)equal to newtons c)not enough information to tell

7
Physics 1D03 - Lecture 37 Concept Quiz Two students are moving a refrigerator. One pushes with a force of 200 newtons (in the positive direction), the other with a force of 300 newtons in the opposite direction. What is the net force ? a)100N b)-100N c) 500N

8
Physics 1D03 - Lecture 38 Coordinate Systems In 2-D : describe a location in a plane by polar coordinates : distance r and angle by Cartesian coordinates : distances x, y, parallel to axes with: x=rcosθ y=rsinθ x y r ( x, y ) 0 x y

9
Physics 1D03 - Lecture 39 Components define the axes first are scalars axes don’t have to be horizontal and vertical the vector and its components form a right triangle with the vector on the hypotenuse x y vyvy vxvx

10
Physics 1D03 - Lecture 310 3-D Coordinates (location in space) y z x y x z We use a right-handed coordinate system with three axes:

11
Physics 1D03 - Lecture 311 x y z Is this a right-handed coordinate system? Does it matter?

12
Physics 1D03 - Lecture 312 Unit Vectors A unit vector u or is a vector with magnitude 1 : (a pure number, no units) Define coordinate unit vectors i, j, k along the x, y, z axis. z y x i j k

13
Physics 1D03 - Lecture 313 A vector can be written in terms of its components: i j Ax iAx i Ay jAy j Ay jAy j Ax iAx i

14
Physics 1D03 - Lecture 314 Addition again: AxAx AyAy ByBy BxBx ByBy BxBx AyAy AxAx CxCx CyCy If A + B = C, then: Three scalar equations from one vector equation! Tail to Head

15
Physics 1D03 - Lecture 315 In components (2-D for simplicity) : The unit-vector notation leads to a simple rule for the components of a vector sum: Eg: A=2i+4j B=3i-5j A+B = 5i-j A - B = -i+9j

16
Physics 1D03 - Lecture 316 Magnitude : the “length” of a vector. Magnitude is a scalar. In terms of components: On the diagram, v x = v cos v y = v sin x y vyvy vxvx e.g., Speed is the magnitude of velocity: velocity = v ; speed = |v| = v

17
Physics 1D03 - Lecture 317 Summary vector quantities must be treated according to the rules of vector arithmetic vectors add by the triangle rule or parallelogram rule (geometric method) a vector can be represented in terms of its Cartesian components using the “unit vectors” i, j, k these can be used to add vectors (algebraic method) if and only if:

Similar presentations

Presentation is loading. Please wait....

OK

Introduction to Vectors

Introduction to Vectors

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Download ppt on acids bases and salts class 10 Ppt on population census 2011 india Ppt on waves physics class 11 Free ppt on phrases and clauses Ppt on forward rate agreement pdf Convert doc file to ppt online Ppt on civil engineering projects Ppt on kindness is contagious Ppt on steve jobs leadership style Ppt on nouns for class 5