A FORM OF ATWOOD'S MACHINE 103 



DYNAMICAL EQUATIONS AND DATA 



Putting 



L=loa,d on each side, including pans and string, 

 w= driving weight, 

 P= weight of revolving pulley, 

 p effective radius of pulley, 

 &=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( I -) asinX, and we 



V 0/ 



readily obtain the well-known result 



- sn X++Gr sn 

 P 



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 



7/J 



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



Zi 



g p 



u 



2L+w+P 2 



Hence equation (1) reduces to the very simple form 



(2) 



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



