I33-] ROTATION. 67 



In engineering practice it is customary to take a whole revo- 

 lution as angular unit and to express the angular velocity of 

 uniform motion by the number of revolutions made in the unit 

 of time. Let n, N be the numbers of revolutions per second 

 and per minute, respectively ; then we have evidently 



(0 



131. When the rotation is not uniform, the quotient obtained 

 by dividing the angle of rotation by the time in which it is 

 described, gives the mean, or average, angular velocity for that 

 time. 



The rate of change of the angle of rotation with the time at 

 any particular moment is called the angular velocity at that 

 moment. By reasoning in a similar way, as in Art. 99, it will 

 be seen that its mathematical expression is 



132. The rate at which the angular velocity changes with the 

 time is called the angular acceleration ; denoting it by , we have 



133. The most important special case of variable angular 

 velocity is that of uniformly accelerated (or retarded) rotation 

 when the angular acceleration is constant. The formulae for 

 this case have precisely the same form as those given in Arts. 

 107-1 n for uniformly accelerated rectilinear motion. Denoting 

 the constant linear acceleration by/, we have, when the initial 

 velocity is o, 



FOR TRANSLATION: FOR ROTATION: 



v =jt, co = at, 



e=*t\ (6) 



