273-J PLANE MOTION. ! 5 ! 



point of intersection of 4 7 with 5 6 can be used to connect with 

 the pump rods of the engine. 



7. ACCELERATIONS IN THE RIGID BODY. 



272. To find the accelerations of the various points of a 

 rigid body we must compare the velocities of these points 

 during two consecutive elements of time ; the change of the 

 velocity divided by dt gives the acceleration. 



In the case of translation (Art. 250) the accelerations of all 

 points of the body are evidently equal so that the acceleration 

 of any point may be called the acceleration of the body. 



273. In the case of rotation about a fixed axis /, any point P 

 of the body at the distance r from the axis describes during the 

 element of time dt a space element ds rdQ = wrdt proportional 

 to this distance r, where a) = d9/dt is the angular velocity of the 

 body about the axis /. The linear velocity of P is v = cor. The 

 :space element ds' described during the next element of time is 

 an infinitesimal arc of the same circle of radius r, i.e. 



ds' = rdO' = r(w + dw) dt. 



Drawing from any point O (Fig. 69) the vectors OV=ds/dt, 

 >OV = ds'/dt, and resolving the ele- 

 mentary acceleration VV[ parallel to 

 the tangent and normal of the path V 



into TV = dv = rda> and VT=vdO = 



ratdO ra) 2 dt, we find the tangential 



and normal components of the accel- Fig< 69 



oration of P by dividing these ele- 



ments by dt. Hence denoting the angular acceleration d<o/dt 



by a, we have 



(0 



The total acceleration of P, 



(2) 



