Page 32 - Schaum's Outline of Theory and Problems of Applied Physics

CHAPTER 2

Vectors

SCALAR AND VECTOR QUANTITIES

A scalar quantity has only magnitude and is completely specified by a number and a unit. Examples are mass
(a stone has a mass of 2 kg), volume (a bottle has a volume of 1.5 liters), and frequency (house current has a
frequency of 60 Hz). Symbols of scalar quantities are printed in italic type (m = mass, V = volume). Scalar
quantities of the same kind are added by using ordinary arithmetic.
A vector quantity has both magnitude and direction. Examples are displacement (an airplane has flown
200 km to the southwest) and velocity (a car is moving at 60 km/h to the north). Another familiar vector
quantity is force. A force is often spoken of as a push or a pull. There is more to the idea of force than this (see
Chapter 5), but it is enough for the exercises in this chapter. Forces give rise to all changes in motion: a force is
needed to start a stationary object moving, to change its direction of motion, and to stop it. We must know the
direction of a force as well as its magnitude to determine what its effects will be. The weight of an object is the
gravitational force that pulls it down toward the earth. The SI unit of force is the newton (N), which is equivalent to
0.225 lb.
Symbols of vector quantities are printed in boldface type (v = velocity, F = force) and expressed in hand-
writing by arrows over the letters ( , F). The magnitude of a vector quantity is printed in italic type (F is the
v

magnitude of the force F). When vector quantities are added, their directions must be taken into account.

VECTOR ADDITION: GRAPHICALMETHOD
A vector is an arrowed line whose length is proportional to a certain vector quantity and whose direction indicates
the direction of the quantity.
To add vector B to vector A, draw B so that its tail is at the head of A. The vector sum A + B is the vector
R that joins the tail of A and the head of B (Fig. 2-1). Usually R is called the resultant of A and B.
The order in which A and B are added is not significant, so that A + B = B + A (Figs. 2-1 and 2-2).
Exactly the same procedure is followed when more than two vectors of the same kind are to be added. The
vectors are strung together head to tail (being careful to preserve their correct lengths and directions), and the

Fig. 2-1
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