XVi 



INTRODUCTION TO MECHANICS. 



round which they are compelled to move. The point to which the 

 motion of a small body, such as the ball with the string 1 , is confined, 

 becomes the centre of its motion ; for it may be considered as moving in 

 the same plane or flat surface. But when a body is not of a size or 

 shape to allow of our considering every part of it as moving in the 

 same plane, it revolves round a line, which is called the axis of motion. 

 In a top, for instance, when spinning- on its point, the axis is the line 

 which passes through the middle of it, perpendicularly to the floor. 

 The axle of the flyers of the windmill is the axis of its motion. The 

 centre of motion is not always in the middle of a body. 



The middle point of a body is called its centre of magnitude, that is, 

 the centre of its mass or bulk. Bodies have also another centre, called 

 the centre of gravity, which shall be explained ; but, at present, we 

 must confine ourselves to the axis of motion. This line remains at rest, 

 whilst all the other parts of the body move around it ; when a top is 

 spun, the axis is stationary, whilst every other part is in motion round it. 

 A top, it is true, has also generally a motion forwards, besides its 

 spinning'motion ; and then no point within it can be at rest. But what is 

 said of the axis of motion relates only to circular motion ; that is, to motion 

 round a line, and not to that which a body may have at the same time 

 in any other direction. 



There is one circumstance in circular motion, which must be carefully 



Fig. 11. 



attended to ; it is, that the further any 

 part of a body is from the axis of mo- 

 tion, the greater is its velocity : as you 

 approach that line, the velocity of the 

 parts gradually diminishes till you reach 

 the axis of motion, which is perfectly at 

 rest. The extremities of the vanes of a 

 windmill move over a much greater 

 space than the parts nearest the axis 

 of motion (Jig. 11). The three dotted 

 circles describe the paths in which three 

 different j>arts of the vanes move, and 

 though the circles are of different dimen- 

 sions, the vanes describe each of them 

 in the same space of time. 

 The force which confines a body to a centre, round which it moves, 

 is called the centripetal force ; and the force which impels a body 

 to fly from the centre, is called the centrifugal force: in circular 

 motion, these two forces balance each other ; otherwise the revolv- 

 ing body would either approach the centre or recede from it, ac- 

 cording as the one or the other prevailed. And should any cause 

 destroy the centripetal force, the centrifugal force would impel the body 



to fly off from the centre. It would not, 

 however, fly off in a right line from the 

 centre ; but in a right line in the direction 

 in which it was moving at the instant of 

 its release : if a stone, whirled round in a 

 sling, gets loose at the point A (Jig. 12), it 

 flies off in the direction A B : this line is 

 called a tangent; it touches the circumfe- 

 rence of the circle, and forms a right angle 

 with a line drawn from that point of the 



