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DEPT, oy APPLIED Roe CHA h 
CHAPTER II 
MOTION AND FORCE 
16. Rest and Motion.—One point A is said to be jixed or to be at 
rest in relation to another point B when the straight line AB does not 
alter in length or direction. If the straight line AB changes in length 
or direction, then A is said to move or have motion in relation to B, If 
* the straight line AB changes in length but not in direction, A has 
rectilinear motion in relation to B, and if AB changes its direction but 
not its length, A has angular or rotary motion in relation to B. If AB 
changes both in length and direction, then A has both rectilinear and 
angular motion in relation to B. Motion is therefore change of position, 
‘but since position can only be defined in relation to points or bodies 
which are fixed or whose motions are neglected, all motion is relative 
motion. 
A point is said to have plane motion when, while it changes its 
position, it remains in the same plane. Of the many problems on 
motion which the engineer has to consider, those on plane motion are by 
far the most common. In an ordinary steam-engine, for example, all the 
points in the piston, piston-rod, cross-head, connecting-rod, crank, crank 
shaft, fly-wheel, eccentric, eccentric-rod, and valve have plane motion. 
The points in the piston, piston-rod, and cross-head have rectilinear 
- motion ; the points in the crank, crank shaft, and fly-wheel have angular 
motion ; and the points in the connecting-rod have both rectilinear and 
angular motions. . 
17. Velocity.—The rate of motion, or rate of change of position of a 
point or body, is called the velocity of the point or body. When the 
changes in position are the same in equal intervals of time,. however 
short these intervals may be, the point or body has uniform velocity. 
When the changes in position are not equal in all equal intervals of 
time, the point or body has variable velocity. At any instant the velocity 
‘of a moving point is completely known when (1) the direction in which 
the point is moving, (2) the rate at which it is moving in that direction, 
and (3) the sense, are known. For example, a point may be moving (1) 
in a direction perpendicular to the surface of still water, (2) at a rate of 
so many feet per second, (3) in an upward direction, The statements 
(1), (2), and (3) are required to completely specify the velocity of a 
point. The statement (2) is called the speed of the point, or the magni- 
tude of the velocity. The term velocity is often used in the same sense 
as speed, but modern writers incline to using the term speed as defined 
above. at . 
A velocity may be completely represented by a straight line. The 
direction of the line is the direction’ of ‘the ‘velocity, the length of the 
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