30 GEOMETRY OF MOTION. [57. 



2. ROTATIONS J ROTORS. 



57. When a rigid body has a motion of rotation about a 

 fixed axis, all its points with the exception of those on the axis 

 describe circular arcs whose centres are situated on the axis 

 (Art. 10). 



The elements determining a rotary displacement, or a rotation^ 

 are the axis and the angle of rotation. These elements can be 

 represented by a single geometrical symbol ; we 

 have only to lay off on the axis of rotation a length 

 01 (Fig. 16) representing on some scale the magni- 

 tude of the angle 6. An arrow-head can be used 

 to mark the sense of the angle. It is customary, 

 at least in English works on mechanics, to adopt 

 the counter-clockwise sense of rotation as positive. 

 The arrow-head should then be placed at that end 

 Fi 16 of the line representing the angle 6 from which 

 the rotation appears counter-clockwise in a plane 

 through the other end at right angles to the axis. The arrow 

 then points in the direction in which an ordinary screw moves 

 when turned in the positive sense. 



This geometrical symbol of a rotation, 01, has been called a 

 rotor. It becomes of importance in the case of infinitesimal 

 rotations, as we shall see later (Art. 68). 



58. Two or more rotations about the same axis can evidently 

 be combined into a single rotation about the same axis whose 

 angle is the algebraic sum of the angles of the component 

 rotations (Art. 12). As regards rotations about different axes, 

 we have to distinguish three cases : intersecting axes, parallel 

 axes, and crossing or skew axes. 



It will be shown in the following articles that rotations about 

 intersecting or parallel axes can always be combined into a 

 single rotation which may happen to reduce to a translation. 



Rotations about skew axes cannot in general be reduced to a 



