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Power generated by flywheel?

  1. Oct 6, 2012 #1
    I've got a flywheel spinning at 850RPM. It weighs 112,34g and has a radius of 38mm.
    I want to calculate the Kinetic energy (Ek) it has given in Wh (watt per hour).

    Angular speed: ω = n*2pi()/60 = 850*2pi()/60 = 89,011 rad/s
    Moment of inertia: I = 0,5*m*r2 = 0,5*0,11234Kg*0,038m^2 = 0,00008110948 Kg*m^2
    Kinetic energy: Ek = 0,5*I* ω^2 = 0,5*0,00008110948 Kg*m^2*(89,011 rad/s)^2 = 0,321 Joule = 0,321 Ws = 0,321/3600 = 8,916*10^-5.

    Is this calculation correct?

    I don't understand how this can be possible. Because it can generate at least 300 milliwatt of power. So I expect the kinetic energy in Wh would be directly connected to how much power it outputs in watt. But that's also confusing... if a generator is generating 300 milliwatt... (5 volt and 60 milliamps), it is generating this per hour???
  2. jcsd
  3. Oct 6, 2012 #2


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    I think you mean Watt times hour, as "Watt per hour" is not a unit of energy.

    If you write an "=", both sides should be equal.
    I did not check the numbers (WolframAlpha can do this, for example), the ansatz is correct.

    But not for long. To could generate 300mW electric power for one hour (!), it would need at least 0.3 Wh kinetic energy.

    No. Energy is power multiplied by time.
  4. Oct 6, 2012 #3


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    Yes, your calculation looks right (didn't actually punch it into a calculator), but the issue appears to be regarding an understanding of units:

    1. Wh is not watts per hour, it is watt-hours. There is no such unit as "watts per hour". So a watt-hour is the energy generated using a power of one watt, for an hour. So:

    2. Yes, the power output in miliwatts and the energy in watt-hours are related....by how long it generates power. The flywheel you're using is about the size of a yo-yo, which can spin-up or spin-down in less than a second, with a small flick of the wrist. So while your flywheel can be made to generate a few hundred miliwatts, it can only do it for a few seconds -- certainly not for an hour.

    [edit: d'oh, too slow]
  5. Oct 6, 2012 #4
    It can't run for an hour? You're right, it can run for a few hours before the heat source is depleted. It's a thermodynamic generator. It has a constant speed.
    There is no such thing as watts per hour? You just said wh is the energy generated using a watt for an hour. Exacly, a watt for an hour = watt per hour. per hour = an hour.

    It's not the size of a yo-yo. It is 72mm wide. That's about the size of one and a half aluminum cola bottle. I just don't get it, how the numbers in joule, can be that low... when the energy output is closer to 400 milliwatt. And not 400 milliwatt*second.

    So do you mind to explain: When I measure the voltage and current, and multiply them together, is that the power I get per hour? If so, that should be 0,4W*3600s=1440Ws?
    So the mechanical calculations don't make sense...
  6. Oct 6, 2012 #5


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    If the generator running at constant speed and is powered from a heat source, the flywheel isn't producing any power at all, on average. It might be gaining and losing some kinetic energy during each revolution, if your heat engine doesn't produce a constant power output over the whole revolution. That's what flywheels are meant to do.

    Your calculation says that if you suddenly removed the heat source, the generator would stop in about 1 second, which seems guite reasonable to me.
  7. Oct 6, 2012 #6


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    No, they're not the same in English. "per" in units always implies division. "watt per hour" would be a rate of change of power. For example, if a motor delivers 100 watts of power at time 1:00, then speeds up gradually so it delivers 300 watts at time 1:30, then we would say its power increases at the (average) rate of 200 watts / 0.5 hour = 400 watts per hour (watts/hour).

    On the other hand, if it runs at a steady rate of 100 watts for a half hour, then it delivers (100 watts)(0.5 hour) = 50 watt-hour of energy.
  8. Oct 6, 2012 #7
    So if it runs at a steady rate of 300 milliwats for one hour, then it delivers 300 milliwatts for one hour? Maybe that sounded silly. But if I've calculated that it outputs 300 milliwat second, and the output is always steady... it will deliver 300 milliwatt of power, after generating power for one hour? So if I've got an electronic device rated 300 mW, the 0,3 Ws is actually sufficient, because it's constantly 0,3Ws???

    I'm sorry for this, mess. But it appears it is a matter of a language problem for me.
  9. Oct 6, 2012 #8


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    Are you perhaps confused about the difference between "energy" and "power"?

    To make an analogy, compare a motor to a gun that fires bullets. The energy produced by the motor (measured in joules, or watt-seconds, or watt-hours, or horsepower-hours) during a certain period of time is analogous to the total number of bullets fired by the gun during that period of time. The power produced by the motor (measured in watts or horsepower) is analogous to the rate at which the gun fires bullets: bullets/second (bullets per second) or bullets/hour (bullets per hour) or something similar. We can talk about the instantaneous power (or rate at which the gun fires bullets) at a certain point of time. We cannot talk about the energy or number of bullets "at" a certain point in time, although we can talk about the energy or total number of bullets during a certain period of time.
  10. Oct 6, 2012 #9
    I think I understand what you mean. And yes, the difference between energy and power IS confusing. Thank you so much for your time. Sincerely.
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