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300 MECHANICS.
The constant force which has to be exerted at any radius,
r, in order to bring the body from a state of rest to an angular
velocity VA in T seconds will be :
r T
R = Constant resistance in pounds.
F = Constant force in pounds.
V& = Angular velocity in feet per second.
/ = Moment of rotation (also called moment of inertia).
r — Radius in feet at which the force is applied.
T = Time in seconds that the force is acting.
Example.
A fly-wheel making 120 revolutions per minute and weigh-
ing 483 pounds, is brought to rest in two seconds by a resistance
acting at a six-inch radius. The radius of gyration of the fly-
wheel is 1.2 feet. What is the average force exerted against the
resistance during these two seconds ?
Solution
:
120 revolutions per minute = 2 revolutions per second.
Angular velocity = 6.2832 X 2 = 12.5664 feet per second.
Moment of rotation = 1.2 X 1.2 X
488
— =21.6
32.2
Radius of resistance, 6 inches = 0.5 feet.
R = 12.5664 X 21.6
= mM ds
2 X 0.5
If a rotating body is not bronght to rest, but only reduced
in speed from an angular velocity of Va to Va x
in T seconds,
then the average force or resistance acting at unit radius is :
F = (Fa ~ Fa -
}
-
T
The average force which has to be exerted at any radius at
t feet to reduce the angular velocity from Va. to Va x
* n ^sec-
onds will be :
F _ (Fa - Fai)/
T r
Example.
A fly-wheel on a punching machine weighs 644 pounds, its
radius of gyration is 1% feet, and it makes at normal speed 300
revolutions per minute, but when the machine is punching the
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