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Work done on a rotating body is equal to the change in its kinetic energy. When an electric fan rotates with a constant angular velocity, then its kinetic energy doesn't change. Does it mean that it doesn't consume electrical energy?

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    $\begingroup$ I've removed a number of comments that were attempting to answer the question and/or responses to them. Please keep in mind that comments should be used for suggesting improvements and requesting clarification on the question, not for answering. $\endgroup$
    – David Z
    May 8, 2020 at 20:28
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    $\begingroup$ Pulling the plug would show you. $\endgroup$ May 11, 2020 at 0:40
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    $\begingroup$ If you unplug the fan and then throw it (frisbee-style) out the airlock of your spacecraft into outer space, it can then rotate indefinitely without consuming any energy. $\endgroup$ May 11, 2020 at 2:17
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    $\begingroup$ @JeremyFriesner No, there will still be internal friction. There's a comment on the accepted answer that goes into more detail about what would happen. $\endgroup$
    – nasch
    May 11, 2020 at 15:17
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    $\begingroup$ @nasch as I understand it, internal friction would occur if the fan blades were rotating relative to the motor. But in the thrown-into-space scenario, the motor is rotating with the fan blades (or perhaps the fan blades were removed from the motor entirely), so internal friction shouldn't happen. The fan would keep rotating for the same reason an asteroid keeps rotating. $\endgroup$ May 11, 2020 at 15:34

7 Answers 7

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It definitely does consume electrical energy. Why? Because there's some opposing force faced by it while it rotates, and this force is often known as air drag/air resistance. You can see the effect of air drag once you switch off the fan. The fan decelerates from its original angular velocity until it stops completely. This deceleration is due to the motion opposing air drag. And thus while rotating, the fan continually loses it's kinetic energy (due to the air drag) and this lost energy is primarily converted to heat energy Thus you don't need electricity to change the kinetic energy, rather you need electrical energy to compensate for the energy lost due to the air drag acting on the fan.

Also the air drag is the most common, most general and easy to understand among all the losses experienced by a fan. However there are many other factors which also increase the loss of energy in a fan. Here's an extremely nice flowchart/Sankey diagram showing this:

losses

Source (PDF)

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    $\begingroup$ It makes me happy this source/in depth info-graphic of fan loss of energy exists. Your answer is good too ;) $\endgroup$
    – TCooper
    May 8, 2020 at 23:10
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    $\begingroup$ Mind you, if the fan was running in a vacuum, then, yes, it could continue to rotate infinitely. Except for the friction in the bearings, maybe. $\endgroup$
    – Vilx-
    May 9, 2020 at 10:44
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    $\begingroup$ @Vilx- Assuming it were in space, the angular momentum won't go anywhere, necessarily. The bearing friction will cause some to be lost to heat, but what would end up happening is that the whole fan assembly would start to spin as the blades lost energy to friction. Internal motion of the fan would come to a stop, but the whole thing would end up spinning in space and would likely continue in that state for a very, very long time. $\endgroup$
    – J...
    May 9, 2020 at 14:51
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    $\begingroup$ It is likely the fan has a non-vanishing quadrupole moment. This would add some loss due to gravitational waves. The respective arrow is too thin to be seen :-) $\endgroup$
    – Jens
    May 9, 2020 at 19:59
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    $\begingroup$ That's an approximate Sankey diagram, not a flow chart. $\endgroup$ May 10, 2020 at 15:24
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when rotating at constant speed, the fan disc is continuously performing work on the air drawn through it by imparting momentum to it. To perform that work requires a constant input of energy from the motor, and therefore the motor is continually absorbing electrical power while the fan is running.

Some of that work is wasted in overcoming drag, but most of it is consumed in accelerating air.

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As stated in the other answers, it is true that a fan rotating with a uniform angular velocity consumes electric energy due to the presence of energy dissipation. But it's not only due to the energy transferred to the air molecules (as others state as "air drag"), but also due to other factors like - friction in the bearing, Joule heating and electromagnetic damping in the motor's coil. Electromagnetic damping also has some useful applications (see Eddy current brake).

It must be noted that when we turn off the fan, electromagnetic damping is present only when the AC motor has a permanent magnet. If the magnetic field for the rotation of the shaft is produced by loops of wires instead of a permanent magnet, it would also become zero. In this case the fan is brought to rest solely by friction and loss of energy to air molecules.

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Indeed a rotating fan does not consume any energy to maintain the same angular velocity... in a vacuum. But if a medium is preset (eg. air, water...), its kinetic energy is increasing (that is the scope of a fan!)

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    $\begingroup$ If you are technical, you need a vacuum, a frictionless bearing, total absence of any static charge or magnetic moment when there is no power to the motor and even then you need to ignore general relativity, because the fan will radiate energy by incredibly tiny gravitational waves. $\endgroup$
    – mlk
    May 8, 2020 at 10:53
  • $\begingroup$ @mlk I'm pretty sure you could come up with a viable fan design that has no quadrupol moment and thus does not radiate gravitational waves (not that that would really matter). $\endgroup$
    – Emil
    May 11, 2020 at 13:19
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Does a car need fuel to drive on a motorway?

You already know what happens when you let go of the gas: friction, mostly from the air. This is exactly the same situation. It makes no difference whether the momentum is linear or angular.

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  • $\begingroup$ Does the oscillating fan (the ones that do a to and fro motion to cover the whole room) consume more energy when they are oscillating as compared to when they are at rest (for same rpm of blades)? I mean we aren't running any extra motors, just using the motor used to rotate the blades and connecting it to some gears and get that oscillating effect. But it still seems counterintuitive... $\endgroup$
    – Satya
    Jul 20, 2023 at 3:20
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But that constant angular velocity is not cost free. It has to be maintained. As others have already mentioned. Air drag of the spinning fan, mechanical friction all tend to slow down the fan. You need power to maintain the velocity. That is why most fans are connected directly or indirectly to electrical power source.

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I assume you mean an indoor cooling fan (either stand-alone or a ceiling fan).

You're right that total energy is always conserved but:

  • Kinetic energy is just one type of energy. Heat is relevant here too. Note that heat is basically the kinetic energy of randomly moving particles.
  • The fan is not a closed system. It's connected to the power supply (as you correctly mentioned) and the air in the room (which you appear to forget).

Recall that the purpose of a fan is to accelerate air in the room to provide a draft. This process requires energy.

Specifically, with a fan rotating at constant speed (i.e. most fans that have been powered on for more than ten seconds), where does the power coming from the power supply go?

  • Some of it goes to losses (in the electric motor, due to friction, and acoustic losses). In all of these cases the lost energy is eventually converted to heat. The fan heats up.
  • Some of the power is needed to accelerate the air in the room, increasing the kinetic energy of the air.

Then, what happens to the kinetic energy in the air?

  • Most of it will get dissipated due to the air's internal friction. This heats up the air. Simply put, when the air comes from the fan, the molecules roughly move in one direction (away from the fan). Then as they encounter other air molecules and obstacles, the motion of the individual molecules becomes increasingly unordered until it is completely random. Random motion of molecules is what we call heat.
  • As a side effect the fast air stream of the fan takes away lots of heat from warmer objects it encounters such as people. That might be the reason you turned on the fan in the first place. More on this at livescience.com

Eventually almost all the energy from the fan gets dissipated as heat one way or another. So if your room is well insulated, the temperature will rise.

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