88 ON THE MOTION OF DEVELOPABLE CYLINDERS. 



city of the body about the axis. For this portion then we 

 shall have the expression 



^/iv/r y^\ 



,(m. 



dt\ l dtj 



For the unwound portion the angular velocity about the 

 axis is not the same for each particle. At any instant y 



is the same for each particle, also —~ is the same for each 



at 



particle. The expression of moments for this part will take 



the form 



5-»{;< r,+ * , >.}- 



The geometrical equations will be the same as before. 

 The positive direction of the axis of x is taken vertically 

 downwards. Suppose w, the attached weight, to have n 

 times the mass of the tape, then the equation of motion 

 may be written 



d dx ( 7T2/7 cx(R> z + 7y % ) ) 



dt 'Jt{-¥ + * f =«»»+*»»*> 



dx 

 The coefficient of — may also be written 

 etc 



I /27T 2 E 4 — cV 



4-y\ it 



) 



Writing, for brevity, this in the form F(<r), the equation 

 of motion becomes 



d 

 dt 



z x /dx\ z 



^F [x) + F 1 (x) [j t J = cxgy +gymr'R\ 



