Please show work: Flywheels are large, massive wheels used to store energy. They
ID: 1487689 • Letter: P
Question
Please show work:
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 requires high power. An industrial flywheel (a uniform disk) has a radius of 75 cm and a mass of 250 kg. Its maximum angular velocity is 1200 rpm.
a) A motor spins up the flywheel with a torque of 50 Nm. How long does it take the flywheel to reach top speed?
b) How much energy is stored in the wheel?
c) The flywheel is disconnected from the motor and connected to a machine that will use its energy. Half of the flywheel’s energy is delivered to the machine in 2 sec. What is the power delivered to the machine?
Explanation / Answer
Here,
mass of wheel , m = 250 kg
angular speed , w = 1200 rpm
radius ,r = 75 cm
r = 0.75 m
a)
moment of inertia , I = 0.5 * m * r^2
I = 0.5 * 250 * 0.75^2 kg.m^2
I = 70.13 Kg.m^2
final angular speed , wf = 1200 rpm
wf = 1200 * 2pi/60 rad/s
wf = 125.7 rad/s
let the time taken is t
using second law of motion
I * (wf - wi) = T * time
70.13 * (125.7 - 0) = 50 * t
t = 176.3 s
the time taken for the flywheel is 176.3 s
b)
energy stored = 0.5 * I * w^2
energy stored = 0.5 * 70.13 * 125.7^2
energy stored = 554044.18 J
the energy stored in the wheel is 554044.18 J
c)
time taken , t = 2 s
Power = energy delivered/time
Power = 554044.18/(2 * 2)
Power = 138511 W
the power delivered to the flywheel is 138511 W