34 THE HUMAN MOTOR 



curvature at M' ; because 



, AC d* 



AC = v da., and -jr = v - 

 at at 



7 A Q jj2 



on the other hand = - ; therefore : = (fig- 58). 

 dt R at K 



When the moving body has to describe a circle with a uniform 

 movement, the tangential acceleration is zero, and .only the 

 centripetal acceleration need be considered, 



,. .. '.'. /=; ... ., . ; , . '. ' 



The centripetal force will be : 



F = mf = m T? 



In fact, that force is a reaction. In considering an example 

 such as a stone in a sling, it will be seen that 

 it exerts a pull on the string along the radius 

 OM and creates there a reaction (tension) ; 

 this is the centrifugal force equal to the 

 centripetal force (fig. 59) . Centrifugal force 

 appears in rapid movements of rotation, 

 causing the rupture of fly-wheels and of 

 millstones ; it obliges the circus rider to 

 lean towards the inside of the track, rails 

 FIO. 59. to be raised on the outer sides of curves 



(superelevation of the permanent way) ; it 



explains the operation of centrifugal drying machines and the 



performance of certain acrobatic feats, such as the so-called 



looping the loop by a cyclist. 



26. Pendulum. The pendulum is a material point which 



swings / at the end of an inextensible wire 



fixed at the opposite end. This movement is 



circular, but on an arc of a circle only (fig. 60). 



The pendulum having been taken to M x , 

 is released and will oscillate from M x to M 2 , 

 the duration of this single oscillation being 



t = 



I represents the length of the pendulum and 

 the oscillations are presumed to be small. 



The theory of the pendulum makes it necessary to resort to 

 the integral and differential calculus which should not be employed 

 in an elementary treatise. But it must be shown that the inten- 

 sity of gravity in the formula can, inversely, be deduced from the 



