Flywheels are large, massive wheels used to store energy. They can be spun up sl
ID: 1501162 • Letter: F
Question
Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.3 m diameter and a mass of 225 kg. Its maximum angular velocity is 1300 rpm.
(a) A motor spins up the flywheel with a constant torque of 60 N · m. How long does it take the flywheel to reach top speed?
(b) How much energy is stored in the flywheel?
(c) The flywheel is disconnected from the motor and connected to a machine to which it will deliver energy. Half the energy stored in the flywheel is delivered in 2 seconds. What is the average power delivered to the machine?
(d) How much torque does the flywheel exert on the machine?
Explanation / Answer
here
mass of disk , m = 225 Kg
radius , r = 1.3/2 = 1 = 0.65 m
angular speed , w = 1300 rpm
w = 136.11 rad/s
a)
let the time taken is t
Using second law of motion
I * w = Torque * time
0.5 * 225 * 0.65^2 * 136.11 = 60 * t
t = 107.8 s
the time taken to reach 1300 rpm is 107.8 s
b)
Energy stored in the flywheel = 0.5 * I * w^2
Energy stored in the flywheel = 0.5 * 0.5 * 225 * 0.65^2 * 136.11^2
Energy stored in the flywheel = 440280.3 J
c)
average power delivered = 0.5 * energy/time
average power delivered = 0.5 * 440280.3/2
average power delivered = 110070.075 W
d)
let the torque applied on the machine is T
I * (wf - wi) = Torque * time
0.5 * 225 * 0.65^2 * (136.11/sqrt(2) - 136.11) = T * 2
solving for T
T = -947.4 N.m
the torque acting on the machine is 947.4 N.m