ROT 



Let r radius of pulley, w its weight, x distance of the centra 

 of gyration from its centre ; then 



2g X (P W) * - (P 4. W) v* 4. w v* X ^ 

 ~ (P 4. W) uz -{- iv. j, but * = -il, 



2P4-2W4- w' 



2?.r. 4. Let A andB represent a single fixed 

 and moveable pulley as represented in the an- 

 nexed figure ; required the space which the de- 

 scending- weight P describes in a given time. 



Let w = weight of each pulley, v = 

 velocity of P, then ~ velocity of W ; also 

 : velocity of the centre of gyration of 

 A, and - g velocity of the same centre 

 in C ; then. 



fo 



PO 



,-W.^-) =P V + W X^ + wX^ 



Ex. 5. A sphere D, whose 

 radius is <> and weight W, is 

 put in motion by a weight P 

 acting by means of a string 

 going over awheel whose ra- 

 dius is r: required the velo. 

 city acquired in the time t. 



Let ?> = velocity of P, s the 

 space descended by P in t", 

 A' distance of the centre of gyration of the sphere from ita centre 

 then 



* X ~* ; but x - ? X 

 P 



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