ii.] LINEAR MOTION. 5 



point of the body fully represents the displacement of the 

 whole body. The translation M Q M 1 of a rigid body M from a 

 position MQ to a position M^ is therefore measured by the 

 rectilinear segment P Q P 1 that represents the displacement of 

 any point P of the body M. 



Two or more consecutive translations of a rigid body in the 

 same direction produce a resultant displacement of translation 

 equal to the algebraic sum of the components. 



10. When a rigid body has two of its points fixed, the only 

 motion it can have is a rotation about the line joining the fixed 

 points as axis. In a motion of rotation all points of the body 

 excepting those on the axis describe arcs of circles whose centres 

 lie on the axis while the points on the axis are at rest. 



The different positions of a rotating body may be referred 

 to any fixed plane passing through the axis of rotation. Any 

 plane of the body passing likewise through the axis will make 

 with the fixed plane an angle 6 which varies in the course 

 of the motion. This angle, taken with the proper sign, fully 

 determines the positions of the body. 



Let the body rotate from a position to a position 6^ ; the 

 angle 0-^ 0^ measures the corresponding displacement, or the 

 rotation, just as (Art. 7) the distance P Q P l =^ l x measures 

 the displacement of a point, and hence (Art. 9) the translation 

 of a rigid body. 



Two or more consecutive rotations of a rigid body about the 

 same axis give a resultant rotation whose angle is the algebraic 

 sum of the angles of the component rotations. 



11. The particular case when the rigid body is a plane figure 

 whose motion is confined to its plane deserves special mention. 

 If one point of such a figure be fixed, the figure can only have 

 a motion of rotation, every other point of the figure describing 

 an arc of a circle whose centre is the fixed point. This point 

 is therefore called the centre of rotation. The positions of the 

 figure are given by the angle that any line of the figure passing 



