^ 



THE HUMAN MOTOR 



(M M' 



fro. 1 



The line MM 7 is called^a " vector " ; M is its origin, M' its 

 extremity (it is marked with an arrow). Hence the vector MM' 

 (from the Latin : vehere, to^carry) represents in magnitude, 

 direction, and sense the speed of the moving point. If the speed 

 is reversed in direction, the vector will have its origin at M', and 

 its extremity at M. 



In the case of a curvilinear movement, fig. 7, the moving point 

 passes from M to M ' in the time t. The speed of the point when 

 in the position M may thus be regarded as its speed when moving 

 along an extremely short chord (shown in dotted lines). This 

 chord, when produced is, in fact, the tangent to the curved path 

 at the position M and the vector representing the velocity at this 

 position will be the tangent MV. 



Similarly the velocity at another position, M", will be repre- 

 sented by a vector M" V", which is a tangent to the path of the 

 moving point at the position M*. 



If the motion of the point is at uniform velocity, 

 Vector MV = vector M"V". 



In the case of variable velocity the vectors MV and M'V" will 

 be of different lengths proportional to the velocities of the point 

 at M and M" respectively. When a point or body is moving along 

 a curvilinear path the vectors representing its velocity at different 

 stages of its movement are always tangential to the path and the 

 actual instantaneous velocities of the point are also along tangents, 

 as will, be seen when a stone describing a circular path in a sling 

 is released, the stone flying off at a tangent to the path. 



In the same way, acceleration can be represented as a vector ; 

 we shall come across other examples later. The advantage of 

 this method of representation is, that it is capable of the widest 

 application. Suppose a moving point takes a direction AB in 

 relation to a line XX '. If it remains in the same plane as the 

 two lines, its speed for example, will be MV along one of them, 

 but in relation to the other it will be the projection MV' of MV. 

 It will be understood, without further explanation that the pro- 

 jection can be made by dropping a line through V perpendicular 

 to XX' (fig. 8). 



