AN'D VIBEATION OF SHAFTS. 
285 
The following table gives the dimensions and other necessary information. In it 
the notation used is as follows :— 
W = Weight of pulley, 
r = Moment of inertia (= A — B). 
h' = (A — B), where g = 32'2. 
E = Young’s Modulus. 
I = Geometrical moment of inertia of cross-section of shaft about a diameter. 
j 
i 
i Name 
: of 
pulley. 
1 
Web. 
Nave. 
W. 
r. 
f/EI 
w^ ■ 
El 
I' ■ 
ft 
Diametei- 
in 
incbes. 
Thickness 
in 
inches. 
Diameter 
in 
inches. 
Length 
in 
inches. 
I. 
II. 
30050 
3-5134 
•0497 
•0882 
•46 
•488 
•622 
•738 
•1216 
•2735 
•00001207 
•0000403 
•003197 
•004745 
9681 
4303 
3,028,000 
906,700 
The pulleys were bored so as to lit the largest part of the shaft, being kept in 
position on it by rubbing bees-wax on the part of the shaft required, and heating the 
pulleys sufficiently to melt the wax. On cooling, the wax was sufficient to firmly 
secure the pulley in its place. 
It may be mentioned that Pulley I. is the model of light pulleys generally used in 
workshops; whilst Pulley II. is the model of a 3-feet belt pulley, weighing about 
500 lbs. In designing the experimental pulleys, account has, of course, been taken of 
the different sized shafts on which the actual pulleys run—the pulleys being designed 
for weight and inertia. 
The following are the actual sizes of the pulleys, of which I. and II. are models :— 
Model pulley. 
Diametei’ of shaft, 
ill 171S. 
Weight of actual 
pulley, in lbs. 
Moment of 
inertia. 
I. 
“4 
95 
•716 
II. 
3 
490 
10-04 
CHAPTER II.—GENERAL THEORY, AS GIVEN BY PROFESSOR REYNOLDS. 
7. Take the axis of x to be the original alignment of the shaft; and that of y per¬ 
pendicular to it and revolving with the shaft. 
