101-2b
In this section, we cover the fundamental concept of Scalars and Vectors
First off, what is a quantity?
A quantity is a measure of certain physical events or instances that are inherently present in the natural world.
Now to this extent we ask, how do we measure these quantities?
A scalar is a physical quantity that is defined solely based on it's magnitude.A vector is a physical quantity that is defined based on both it's magnitude and it's direction.
To elaborate, in order for a quantity to be considered a vector, the physical or numerical values considered to define it, it must be accompanied by a secondary set of value that provide the necessary data on the direction or orientation of that quantity in physical space.The fundamental quantities, are all scalar quantities i.e Mass, Length, Time etc.
The derived quantities, such as Force, Displacement, Velocity etc. are vectors.The difference is more imperative when considering specific quantities w.r.t the world co-oordinate systems, so as to improve upon anything physical.
In this section, we cover the fundamental concept of Scalars and Vectors
First off, what is a quantity?
A quantity is a measure of certain physical events or instances that are inherently present in the natural world.
Now to this extent we ask, how do we measure these quantities?
A scalar is a physical quantity that is defined solely based on it's magnitude.A vector is a physical quantity that is defined based on both it's magnitude and it's direction.
A particle moving along a straight line can move in only two directions. We can
take its motion to be positive in one of these directions and negative in the other.
For a particle moving in three dimensions, however, a plus sign or minus sign is no
longer enough to indicate a direction. Instead, we must use a vector.
A vector has magnitude as well as direction, and vectors follow certain (vector) rules of combination, which we examine in this chapter. A vector quantity is a quantity that has both a magnitude and a direction and thus can be represented with a vector. Some physical quantities that are vector quantities are displacement, velocity, and acceleration. You will see many more throughout this book, so learning the rules of vector combination now will help you greatly in later chapters.
Not all physical quantities involve a direction. Temperature, pressure, energy, mass, and time, for example, do not “point” in the spatial sense. We call such quantities scalars, and we deal with them by the rules of ordinary algebra. A single value, with a sign (as in a temperature of 40°F), specifies a scalar.
The simplest vector quantity is displacement, or change of position. A vector that represents a displacement is called, reasonably, a displacement vector. (Similarly, we have velocity vectors and acceleration vectors.) If a particle changes its position by moving from A to B in, we say that it undergoes a displacement from A to B, which we represent with an arrow pointing from A to B. The arrow specifies the vector graphically. To distinguish vector symbols from other kinds of arrows in this book, we use the outline of a triangle as the arrowhead.
The arrows from A to B, from A to B , and from A to B have the same magnitude and direction. Thus, they specify identical displacement vectors and represent the same change of position for the particle. A vector can be shifted without changing its value if its length and direction are not changed.
The displacement vector tells us nothing about the actual path that the particle takes. For example, all three paths connecting points A and B cor- respond to the same displacement vector, that of the Displacement vectors represent only the overall effect of the motion, not the motion itself.
A vector has magnitude as well as direction, and vectors follow certain (vector) rules of combination, which we examine in this chapter. A vector quantity is a quantity that has both a magnitude and a direction and thus can be represented with a vector. Some physical quantities that are vector quantities are displacement, velocity, and acceleration. You will see many more throughout this book, so learning the rules of vector combination now will help you greatly in later chapters.
Not all physical quantities involve a direction. Temperature, pressure, energy, mass, and time, for example, do not “point” in the spatial sense. We call such quantities scalars, and we deal with them by the rules of ordinary algebra. A single value, with a sign (as in a temperature of 40°F), specifies a scalar.
The simplest vector quantity is displacement, or change of position. A vector that represents a displacement is called, reasonably, a displacement vector. (Similarly, we have velocity vectors and acceleration vectors.) If a particle changes its position by moving from A to B in, we say that it undergoes a displacement from A to B, which we represent with an arrow pointing from A to B. The arrow specifies the vector graphically. To distinguish vector symbols from other kinds of arrows in this book, we use the outline of a triangle as the arrowhead.
The arrows from A to B, from A to B , and from A to B have the same magnitude and direction. Thus, they specify identical displacement vectors and represent the same change of position for the particle. A vector can be shifted without changing its value if its length and direction are not changed.
The displacement vector tells us nothing about the actual path that the particle takes. For example, all three paths connecting points A and B cor- respond to the same displacement vector, that of the Displacement vectors represent only the overall effect of the motion, not the motion itself.
The derived quantities, such as Force, Displacement, Velocity etc. are vectors.The difference is more imperative when considering specific quantities w.r.t the world co-oordinate systems, so as to improve upon anything physical.
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