IMPULSE AND MOMENTUM Machinery's Handbook, 31st Edition
193
where ω f and ω o are the final and initial angular velocities, respectively. Example: A flywheel having a moment of inertia of 25 lbs-ft-sec 2 is revolving with an angular velocity of 10 rad/sec, when a constant torque of 20 lbs-ft is applied to reverse its direction of rotation. For what length of time must this constant torque act to stop the flywheel and bring it up to a reverse speed of 5 rad/sec? Solution: Applying Formula (5c),
. T t J t t 20 25 10 5 250 125 375 20 188 seconds o M f o ' ~ ~ = − = − − = + = = ^ ^ h h 6 @
A similar example using metric SI units is as follows: A flywheel with a moment of inertia of 20 kg-m 2 is revolving with an angular velocity of 10 rad/s when a constant torque of 30 N-m is applied to reverse its direction of rotation. For what length of time must this constant torque act to stop the flywheel and bring it up to a reverse speed of 5 rad/s? Applying Formula (5c), the calculation is: T o t J M ω f ω o – ( ) = 30 t 20 10 5 – – ( ) = Thus, t 20 15 × 30 = --------- = 10s Formulas for Work and Power.— The formulas in the accompanying Table 4 may be used to determine work and power in terms of the applied force and the velocity at the point of application of the force. Table 4. Formulas a for Work and Power To Find Known Formula To Find Known Formula
P , t , F S = P 3 t ÷ F
F , S P , t
K = F 3 S K = P 3 t
K , F
S = K ÷ F
S
K
t , F , hp S = 550 3 t 3 hp ÷ F
F , V , t t , hp F , S , t
K = F 3 V 3 t K = 550 3 t 3 hp hp = P ÷ 550 hp = F 3 V ÷ 550 hp = K ÷ (550 3 t ) hp = F 3 S ÷ (550 3 t )
P , F
V = P ÷ F
K , F , t F , hp
V = K ÷ ( F 3 t ) V = 550 3 hp ÷ F
V
P
hp
F , S , P t = F 3 S ÷ P K , F , V t = K ÷ ( F 3 V ) F , S , hp t = F 3 S ÷ (550 3 hp )
F , V K , t
t
Meanings of Symbols: (metric units see note a )
P , V K , S
F = P ÷ V F = K ÷ S
F
S = distance in feet V = constant or average velocity in ft/sec t = time in seconds F = constant or average force in pounds P = power in foot-pounds per second hp = horsepower K = work in foot-pounds
K , V , t V , hp F , V F , S , t
F = K ÷ ( V 3 t ) F = 550 3 hp ÷ V
P = F 3 V P = F 3 S ÷ t
P
K , t
P = K ÷ t
P = 550 3 hp
hp
Copyright 2020, Industrial Press, Inc.
ebooks.industrialpress.com
Made with FlippingBook - Share PDF online