CHAPTEE XI 

 MOTION OF RIGID BODIES 



229. The present chapter is devoted to a discussion of the 

 motion of rigid bodies, when the motion is such that the bodies 

 may not be treated as particles. 



It has already been proved in 66 that the most general motion 

 possible for a rigid body is one compounded of a motion of trans- 

 lation and a motion of rotation. As a preliminary to discussing 

 the general motion of a rigid body under the action of forces of 

 any description, we shall examine in greater detail than has so far 

 been done the properties of a motion of rotation. 



ANGULAR VELOCITY 



230. We have seen (67) that for every motion of a rigid body 

 in which a point P remains fixed, there is an axis of rotation, 

 which is a line passing through P, of which every point remains 

 fixed. If a rigid body is moving continuously we may analyze its 

 motion in the following way. We select a definite particle P of 

 the rigid body, and we refer the motion to a frame of reference 

 having P as origin, and moving so as always to remain parallel 

 to its original position. Eelative to this frame, the motion of the 

 body between any two instants is a motion of rotation about P. 



Now let the two instants be taken very close to one another, 

 the interval between them being dt. Let us find the axis of rota- 

 tion of the motion which takes jplace in the interval dt, and call it ' 

 PQ. Then PQ is called the axis of rotation at the instant at which 

 the interval dt is taken. 



Let us suppose that during the interval dt the rotation of the 

 body about its axis of rotation PQ is found to be a rotation 



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