298.] THE RIGID BODY. 



3. ACCELERATIONS IN THE RIGID BODY. 



297, The accelerations of the points of a rigid body are 

 found by comparing the velocities of these points during two 

 successive elements of time. 



If the motion of the rigid body be a pure translation, all 

 points of the body describe equal and parallel curves. The 

 accelerations of all points being equal and parallel (Art. 272), 

 the acceleration j of any one point of the body can be spoken 

 of as the acceleration of the body. It can be resolved into a tan- 

 gential component j t along the tangent to the path of any point 

 and a normal component / along the normal to the path, and we 

 have, just as in Art. 159, 



(i) 



298. If the motion of the rigid body be a pure rotation about 

 the same axis / for at least two successive elements of time dt t 

 all points describe arcs of circles whose centres lie on the fixed 

 axis /. As shown in Art. 273, the acceleration j of any point P 

 whose distance from / is r can be resolved into a tangential 

 component j t perpendicular to the plane (/, P) and a normal com- 

 ponent / at right angles to the axis /; and we have (Art. 273) 



(2) 



where is the angular velocity and a = da)/dt the angular 

 acceleration of the body. 



The normal component / being always directed towards the 

 axis of rotation / is sometimes called the centripetal acceleration. 



