170 



KINEMATICS. 



[302. 



to /in the plane (/, /'). This is equivalent to resolving the rotor 

 w + do> along /' into the rotors to + du> along /and a>d<j along ;/. 



The body can now be regarded as rotating during both ele- 

 ments of time about the axis /, viz. during the first element 

 with angular velocity o>, during the second with angular velocity 

 w + dw, and in addition to that during the second element about 

 the axis n with the infinitesimal angular velocity ndcr. 



(n), 



Fig. 78. 



The rotation about /(Art. 298) produces, for points at unit 

 distance from /, a centripetal acceleration o> 2 perpendicular to /and 

 a tangential acceleration dw/dt which may be represented by a 

 rotor dw/dt along /. The rotation about n gives to points at 

 unit distance from n an infinitesimal velocity wda at right angles 

 to the planes through n and thus produces an acceleration 

 todvldt^tou which may be represented by a rotor along n. The 

 rotors dwjdt along / and mi along n being at right angles to 

 each other (see Fig. 78), combine to form the angular acceler- 

 ation 



It is apparent that the component da/di of a has the effect 





