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MECHANICS. 299
Angular Velocity.
When a body revolves about any axis, the parts furthest
from the axis of rotation move the fastest. The linear velocity
at a radius of one footfro?n the center of rotation is called the
angular velocity of the body. It is usually reckoned in feet per
second. The angular velocity of any revolving body is ex-
pressed by the formula,
Fa = 2 7T n
V& = Angular velocity in feet per second.
n = Number of revolutions per second.
Rule.
Multiply the number of revolutions per second by 6.2832
and the product is the angular velocity in feet per second.
Example.
What is the angular velocity of a fly-wheel making 300
revolutions per minute ?
Solution
:
300 revolutions per minute = 5 revolutions per second,
therefore, angular velocity = 6.2832 X 5 =31.416 feet per
second. Angular velocity expresses the linear velocity at unit
distance from center of rotation and in English measure this unit
is feet. As already stated, the moment of rotation is an expres-
sion for the mass of the rotating body (theoretically) transferred
to unit distance from center of rotation ; the product of angular
velocity and moment of rotation will, therefore, be the
momentum of the rotating body. The constant resistance
which has to be exerted at unit radius in order to bring the
body to rest in T seconds will be :
R=^l
T
The resistance which has to be exerted at any radius of r
feet to bring the body to rest in T seconds will be
:
R = ^l
r T
R = Resistance in pounds.
Va. = Angular velocity in feet per second.
/ = Moment of rotation (also called moment of inertia).
The constant force which has to be exerted at unit radius
in order to bring the body from a state of rest to an angular
velocity V& in T seconds will be :
’
F - v* I
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