330 APPLIED MECHANICS * 
of which OY is the axis. If AB is a rod, there is a joint at B which per. 4 
mits of the free angular movement of AB about B in the plane AOY. 
As A revolves at a steady speed, AB describes the surface of a cone 
whose vertex is at O, where AB intersects OY, whose height is A, and 3 
whose base has a radius 7. The forces acting on A in the plane AOY 
are, its weight W, the centrifugal force F, and the tension T in AB, and 
for steady motion these must balance one another. Hence, taking 
moments about O, Fh=Wr. But pate ", where o is the a 
4 
’ 
velocity of A about OY, therefore — = Wr, and ha = 
If g is in feet per second per second, and o is in ees per second, 
then hf isin feet. If A Sate m revolutions per second, or N revolutions _ 
6029 a 
Ar oe 4x?N2* 
Referring to Figs, 512 and 513, where the point of suspension B is 
not on the axis OY, if the speed of rotation is given, the height 2 is found 
as above, but there is no simple for- 
mula for calculating 7, nor is there, so 
far as the writer is aware, any direct 
geometrical construction for fixing the 
position of AB. AB must therefore 
be fixed either by trial or by using 
a locus curve. Several locus curves 
may be used, but the one shown in 
Fig. 514 is probably the simplest. 
With centre B and radius equal to AB 
draw the are DE, which must contain 
the point A. Draw PBp, QBg, etc., 
several positions of the axis of the 
arm AB, meeting the axis YY at p, 
q, etc. Make pl, 2, etc., each equal to 
h. Draw horizontal lines through 1, 
2, etc., to meet PB, QB, etc., respec- Fia. 514. 
_ tively. A fair curve drawn through 
the points thus determined will cut the arc DE at a point which is the 
position of A corresponding to the height h. 
283. Effect of Mass of Arm in Revolving Pendulum.—In obtaining 
the result h=g/w? 
in the preceding 
Article, the weight 
and centrifugal 
force of the arm 
were neglected. The 
effect of these will 
now be considered. 
The arm AB will 
be assumed to be 
of uniform § cross 
per minute, then h= 
Fig. 515. Fra: 516. Fie. 517. 
section, and to weigh w Ibs. per foot of length. Its length a will be 
