40 



VELOCITY AND ACCELERATION. 



[CHAP. in. 



These equations may be expressed in words as follows : 



The \ . j, [ of B relative to axes at is compounded 

 (acceleration) 



of the ! . &amp;gt; of A relative to the same axes and the 



(acceleration J 



! , ,. [ of B relative to parallel axes through A. 

 (acceleration) 



The discussion of the motion of B relative to axes whose origin 

 is A but which move so as not to be always parallel to the axes 

 whose origin is at is deferred for the present. 



40. Geometry of Relative motion. The geometrical view 

 of relative motion is instructive, and leads easily to results of 

 some importance. For shortness we shall speak of displacement, 

 velocity, and acceleration of a point relative to a second point, 

 meaning thereby displacement, velocity, and acceleration of the 

 point relative to axes through the second point parallel to the 

 axes of reference. 



Let A be the position at any time t of a point which 

 moves relatively to a frame having its origin at 0, and let A be 

 its position at time t . From draw OH equal and parallel 

 to A A , and in the same sense ; the vector represented by OH is 

 the displacement of A. 



Similarly let B be the position at time t of a second point 

 referred to the same frame, and B its position at time t . From 

 draw OK equal and parallel to BB , and in the same sense ; the 

 vector represented by OK is the displacement of B. 



Fig. 29. 



Then the displacement of B relative to A is the vector that 

 must be compounded with the displacement of A in order that 

 the resultant may be the displacement of B. 



