12 ALTERNATING CURRENTS 



j X 360 = 45. As the wave completes 360 in ^ 5 or 0.04 s<v. in 

 0.005 SIM\ it will* have completed () vy 4 n = J s <>'<!>. 



360/8 = 45 



i' = 42.4 sin 45 = 42.4 X 0.707 = 30 amp. Ana. 



7. Scalars and Vectors. Quantities in general are divided into 

 two classes, scalars and vectors. 



A scalar is a quantity which is completely determined by its 

 magnitude alone. Examples of scalar quantities are dollars, 

 energy, gallons, mass, temperature, etc. Such quantities are 

 added algebraically. For example, two dollars plus five dollars 

 equals seven dollars. 



A vector has direction as well as magnitude. A common ex- 

 ample of a vector is force. When a force is under consideration, 

 not only its magnitude but its direction as well must be consid- 

 ered. When two or more forces are added, they are not neces- 

 sarily added algebraically but must be combined in such a way 

 as to take into consideration their directions as well as their 

 magnitudes. 



Figure 9 (a) shows two forces acting at the point and repre- 

 sented by the vectors FI and F 2 . The length of each of these 

 vectors, to scale, is equal to the magnitude of the force which it 

 represents. The direction of each of these vectors s'hows the 

 direction in which the force acts. is the angle between FI and 

 F 2 . Their sum, F , or the single force which would have the 

 same effect on their point of application, 0, as FI and F 2 acting 

 in conjunction, is called their resultant. F is one diagonal of the 

 parallelogram having FI and F 2 as adjacent sides. 



Figure 9 (6) shows a triangle having F\ and F 2 as two of its 

 sides, FI and F 2 being respectively parallel to, and acting in the 

 same directions as, FI and F 2 of Fig. 9 (a). The exterior angle 

 between FI and F 2 is therefore equal to 0. The third side of the 

 triangle F is equal in magnitude and direction to f of Fig. 9 

 (a). Therefore, the resultant of two vectors may be found by 

 means of a triangle properly constructed, of which two sides are 

 the two component vectors and the third side is their sum. Such 

 a triangle is called a triangle of forces. It is usually simpler to 

 use the triangle of forces than to use the parallelogram of forces. 



To subtract one vector from another, reverse this vector and 



