A FORM OF ATWOOD'S MACHINE 103 



DYNAMICAL EQUATIONS AND DATA 



Putting 



L=\oad on each side, including pans and string, 

 w= driving weight, 

 P=weight of revolving pulley, 

 p= effective radius of pulley, 

 fc=radius of gyration of pulley, 

 a= observed acceleration, 

 a=radius of spindle, 

 and a sin X= effective friction radius, 



the friction moment becomes 2L+P+w(l -) asinX, and we 



V 9' 

 readily obtain the well-known result 



sin 



(I) 



w 



Frictional retardation, a', is determined by observing the time 

 taken to come to rest after communicating a certain speed to 

 the system symmetrically loaded. This is also done on the 

 chronograph, it being now necessary to observe and record on 

 pen No. 3 the moment at which motion ceases. To get as near 

 as possible to the same conditions of load as those obtaining 

 in the actual a experiment, it is well to observe a' with a load 



L'=L+ on each side, and in that case a! is given by 

 2 



a 

 P 



2L+w+P- z 

 P* 



Hence equation (1) reduces to the very simple form 



. . . (2) 



w 

 In this form, viz. Driving Force minus Frictional Force equal to 



