Top-Rated Free Essay

Scalar and Vectors

Satisfactory Essays
Mathematicians and scientists call a quantity which depends on direction a vector quantity, and a quantity which does not depend on direction is called a scalar quantity.
Vector quantities have two characteristics, a magnitude and a direction. Scalar quantities have only a magnitude. When comparing two vector quantities of the same type, you have to compare both the magnitude and the direction. For scalars, you only have to compare the magnitude. When doing any mathematical operation on a vector quantity (like adding, subtracting, multiplying...) you have to consider both the magnitude and the direction. This makes dealing with vector quantities a little more complicated than scalars.
On the slide we list some of the physical quantities discussed in the Beginner's Guide to Propulsion and group them into either vector or scalar quantities. Of particular interest, the forces, which operate on a flying aircraft, the weight, thrust, and aerodynamic forces, are all vector quantities. The resulting motion of the aircraft in terms of displacement, velocity, and acceleration are also vector quantities. These quantities can be determined by application of Newton's laws for vectors. The scalar quantities include most of the thermodynamic state variables involved with the propulsion system, such as the density, pressure, and temperature of the propellants. The energy, work, and entropy associated with the engines are also scalar quantities. There are some quantities, like speed, which have very special definitions for scientists. By definition, speed is the scalar magnitude of a velocity vector. A car going down the road has a speed of 50 mph. Its velocity is 50 mph in the northeast direction. It can get very confusing when the terms are used interchangeably!
While Newton's laws describe the resulting motion of a solid, there are special equations which describe the motion of fluids, gases and liquids, through the propulsion system. For any physical system, the mass, momentum, and energy of the system must be conserved. Mass and energy are scalar quantities, while momentum is a vector quantity. This results in a coupled set of equations, called the Navier-Stokes equations, which describe how fluids behave when subjected to external forces. These equations are the fluid equivalent of Newton's laws of motion and are very difficult to solve and understand. A simplified version of the equations called the Euler equations can be solved for some fluids problems.

You May Also Find These Documents Helpful

  • Satisfactory Essays

    Scalar Vector

    • 299 Words
    • 2 Pages

    Acceleration Velocity Displacement Distance Time Definition 1. Acceleration is the rate of change of velocity with time. Velocity is a vector physical quantity; both magnitude and direction are required to define it. the length of an imaginary straight path, typically distinct from the path actually travelled by P. Distance is a numerical description of how far apart objects are. In physics or everyday usage, distance may refer to a physical length, or an estimation Time in physics is…

    • 299 Words
    • 2 Pages
    Satisfactory Essays
  • Powerful Essays

    Vectors and Scalars

    • 1288 Words
    • 6 Pages

    HL Vectors Notes 1. Vector or Scalar Many physical quantities such as area, length, mass and temperature are completely described once the magnitude of the quantity is given. Such quantities are called “scalars.” Other quantities possess the properties of magnitude and direction. A quantity of this kind is called a “vector” quantity. Winds are usually described by giving their speed and direction; say 20 km/h north east. The wind speed and wind direction together form a vector quantity…

    • 1288 Words
    • 6 Pages
    Powerful Essays
  • Powerful Essays

    Vectors

    • 178782 Words
    • 716 Pages

    Calculus in 3D Geometry, Vectors, and Multivariate Calculus Zbigniew H. Nitecki Tufts University August 19, 2012 ii This work is subject to copyright. It may be copied for non-commercial purposes. Preface The present volume is a sequel to my earlier book, Calculus Deconstructed: A Second Course in First-Year Calculus, published by the Mathematical Association in 2009. I have used versions of this pair of books for severel years in the Honors Calculus course at Tufts, a two-semester…

    • 178782 Words
    • 716 Pages
    Powerful Essays
  • Satisfactory Essays

    Force Vector

    • 2682 Words
    • 11 Pages

    12e 2 Force Vectors Part 2 Copyright © 2010 Pearson Education South Asia Pte Ltd Chapter Objectives • Cartesian vector form • Dot product and angle between 2 vectors Copyright © 2010 Pearson Education South Asia Pte Ltd Chapter Outline 1. 2. 3. 4. 5. Cartesian Vectors Addition and Subtraction of Cartesian Vectors Position Vectors Force Vector Directed along a Line Dot Product Copyright © 2010 Pearson Education South Asia Pte Ltd 2.5 Cartesian Vectors • Right-Handed…

    • 2682 Words
    • 11 Pages
    Satisfactory Essays
  • Satisfactory Essays

    Vector Analysis

    • 429 Words
    • 2 Pages

    Sciences ECE / ICE / MexE Department ECE 352 VECTOR ANALYSIS DEL OPERATOR GROUP 3 Andaya, Rizalyn Ramos, Maria Issa P. ∇ Del is a symbol used in mathematics, in particular, in vector calculus, as a vector differential operator, usually represented by the nabla symbol ∇. Del may denote the gradient (locally steepest slope), the divergence of a vector field, or the curl (rotation) of a vector field. The symbol ∇ can be interpreted as a vector of partial derivative operators, and its three…

    • 429 Words
    • 2 Pages
    Satisfactory Essays
  • Good Essays

    Vector Addition

    • 3189 Words
    • 13 Pages

    Directed Line Segment: VECTORS • A line segment with direction is called a directed line segment. • If ‘A’ and ‘B’ are two distinct points in the space, then the ordered pair (A, B) is called as a directed line segment and is denoted by """""# . ! • In """""# , ‘A’ is called initial point and ‘B’ is called terminal ! point of """""# . ! • The distance from ‘A’ to ‘B’ is called the length or magnitude of """""# . The length or magnitude of """""# ! ! is denoted by '"""""# '. Thus…

    • 3189 Words
    • 13 Pages
    Good Essays
  • Good Essays

    Vector analysis

    • 3612 Words
    • 15 Pages

    Vector Analysis Definition A vector in n dimension is any set of n-components that transforms in the same manner as a displacement when you change coordinates Displacement is the model for the behavior of all vectors Roughly speaking: A vector is a quantity with both direction as well as magnitude. On the contrary, a scalar has no direction and remains unchanged when one changes the coordinates. Notation: Bold face A, in handwriting A . The magnitude of the vector is denoted by A  A …

    • 3612 Words
    • 15 Pages
    Good Essays
  • Good Essays

    Vector Analysis

    • 639 Words
    • 3 Pages

    1.1.1 Show how to find A and B, given A+B and A −B. 1.1.2 The vector A whose magnitude is 1.732 units makes equal angles with the coordinate axes. Find Ax,Ay , and Az. 1.1.3 Calculate the components of a unit vector that lies in the xy-plane and makes equal angles with the positive directions of the x- and y-axes. 1.1.4 The velocity of sailboat A relative to sailboat B, vrel, is defined by the equation vrel = vA − vB, where vA is the velocity of A and vB is the velocity of B. Determine the velocity…

    • 639 Words
    • 3 Pages
    Good Essays
  • Satisfactory Essays

    Vectors Packet

    • 719 Words
    • 3 Pages

    each of the following vectors in terms of and (a) (b) (c) (Total 4 marks) 2. The vectors , are unit vectors along the x-axis and y-axis respectively. The vectors = – + and = 3 + 5 are given. (a) Find + 2 in terms of and . A vector has the same direction as + 2 , and has a magnitude of 26. (b) Find in terms of and . (Total 4 marks) 3. The circle shown has centre O and radius 6. is the vector , is the vector and is the vector . (a) Verify…

    • 719 Words
    • 3 Pages
    Satisfactory Essays
  • Powerful Essays

    Addition of vectors

    • 2645 Words
    • 14 Pages

    Resolution of Vectors Equilibrium of a Particle Overview When a set of forces act on an object in such a way that the lines of action of the forces pass through a common point, the forces are described as concurrent forces. When these forces lie in the same geometric plane, the forces are also described as coplanar forces. A single G G equivalent force known as the resultant force FR may replace a set of concurrent forces F1 and G F2 , as shown. This resultant force is obtained by a process of vector addition…

    • 2645 Words
    • 14 Pages
    Powerful Essays