Flywheels are large, massive wheels used to store energy. They can be spun up sl

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 1.6m diameter and a mass of 220kg . Its maximum angular velocity is 1500rpm.

Part A: A motor spins up the flywheel with a constant torque of 51N?m . How long does it take the flywheel to reach top speed?

Part B: How much energy is stored in the flywheel?

Part 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 2.5s . What is the average power delivered to the machine?

Part D: How much torque does the flywheel exert on the machine?

Explanation / Answer

Part A)

Start with Torque = I(alpha)

I for a disk is .5mr2

Thus T = .5mr2(alpha)

51 = (.5)(220)(.8)2(alpha)

alpha = .724 rad/s2

Then apply wf = wo + alpha(t_

1500 rpm converts to 157.1 rad/s

157.1 = 0 + (.724)(t)

t = 217 sec

Part B)

Energy = .5Iw2

E = (.5)(.5)(220)(.8)2(157.1)2

E = 8.69 X 105 J

Part C)

P = E/t

P = (8.69 X 105)/2(2.5)

P = 1.74 X 105 W

Part D)

P = Tw

(1.74 X 105) = T(157.1)

Torque = 1.11 X 103 Nm

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