I'll. VII ACCELERATION 157 



The time factor can be expressed thus : 



r= 6-4,5 RW~ seconds (87). 



** 



When the motion of the motor shaft is com- 

 municated to the main shaft by a clutch, the 



motor may run at full speed before connection. Let the 

 moment of inertia of the moving portion of the motor, the 

 armature, pulley, &c., be /,, and that of the main shaft with 

 the rotating mass 7 2 . If the motor is running at n } r.p.s. 

 before connection, the kinetic energy of the motor shaft 

 will be 27r 2 vi 1 2 7 1 . If the speed immediately after connection 

 is ?i 2 r.p.s., the kinetic energy will be 2-7r 2 n 2 2 / 1 . The 



difference represents the kinetic energy of the main shaft 



02 

 immediately after connection, and this is - 2 n 2 2 J 2 . 



The reduced speed, n 2 of the motor shaft, is given by 

 the equation 



< 2 = _-] -- V .................. (88). 



After connection the system will begin to accelerate, 

 and the acceleration at any time can be found from Equa- 

 tion 69, with due regard to sign and to the value of r. 

 If the frictional torque is unaltered, the final speed of the 

 motor will be the same as the initial speed. If the fric- 

 tional torque has increased, we can find the new speed by 

 inserting the new value of c f in the equation for n f . 



We may have to design an equipment by which the 

 main shaft can be started up without drawing more than 

 a specified current of c 2 amperes from the line. The 



