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I think it probably has something to do with the capacitor inside but I don't get it why doesn't it just Start spinning instantly when we push the button why does it slowly start to spin and gradually gets faster?

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    $\begingroup$ This seems to be a question about the design of a specific appliance, which is engineering, not physics. $\endgroup$ – ACuriousMind Apr 12 '16 at 10:27
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    $\begingroup$ I think there is an underlying physical principle here (see my answer), which is to do with whether it's possible to even think about a fan which started suddenly. $\endgroup$ – tfb Apr 12 '16 at 10:56
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    $\begingroup$ Why doesn't your car reach highway speed instantly when you push the gas? $\endgroup$ – Phil Frost Apr 12 '16 at 12:15
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    $\begingroup$ I just asked my self is there even anything that happens "instantly"? $\endgroup$ – Zaibis Apr 12 '16 at 13:54
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    $\begingroup$ @Zaibis Some things do. Accelerating something that has a positive mass isn't one of those things, though. $\endgroup$ – reirab Apr 12 '16 at 16:47
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The fan motor provides a torque $\tau$ which has to accelerate $\alpha$ the fan blades whose moment of inertia is $I$: $$\tau=I\alpha$$

Given how long it takes for the fan blades to stop the frictional torques must be fairly low and so the torque applied by the motor to keep them going must also be low. With the relatively small torque rating, even if the motor applied maximum torque when starting from rest, it would still take a noticeable period of time for the blades to reach their final rotational speed.

The capacitors are there to make sure the motor rotates in the right direction when switched on and/or to allow the speed of the motor and hence the blades to be controlled.

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    $\begingroup$ Just to add to this answer: The fan could be made to start faster, but that would mean to use a motor with higher torque and thus higher price (and probably weight), which would increase the price of the fan without much advantage for the buyer. So the reason would be likely a compromise in engineering and business economics. $\endgroup$ – Dubu Apr 12 '16 at 8:47
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    $\begingroup$ In summary: because it's heavy. $\endgroup$ – Jacob Krall Apr 12 '16 at 16:22
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    $\begingroup$ In summary: because it's expensive. $\endgroup$ – corsiKa Apr 12 '16 at 19:20
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    $\begingroup$ @Dubu, it would be more complicated too. The simple construction simply has the torque it needs for the normal operation and the engine runs at the same power from the start, so it spins up and the acceleration decreases as the air resistance builds up. To make it spin up faster, the engine would need higher torque during start than later for normal operation and therefore would additionally need a regulator. $\endgroup$ – Jan Hudec Apr 12 '16 at 20:53
  • $\begingroup$ The drag equation at fan blades speed is probably something like "drag = speed^3" or "drag=speed^4" so "so the torque applied by the motor to keep them going must also be low" is probably not a good assumption. $\endgroup$ – Sam Apr 12 '16 at 21:04
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A much simpler way of thinking about this is to consider energy. When the fan is spinning it has quite a lot of kinetic energy (try to stop it by putting your finger in the way to confirm this (don't actually do this!)). That kinetic energy goes as the square of the rotation rate, in fact.

So as the fan starts, the motor needs to add energy to it. It does this by taking energy from the electricity supply. Well, the amount of energy it takes from the supply per second is the power of the motor. If it is going to start the fan really quickly it needs a great deal of power during the period the fan is spinning up. That means that it would need both enormous cables running to it, and the motor itself would be huge. Once the fan is spinning it needs much less power, so all of this is only needed during the spin-up process.

Economics, as well as the desire not to have enormous motors and cables attached to the ceiling, almost certainly requiring special support beams, possible liquid-cooling arrangements and so on, mean that rather small motors get used, and people live with a few seconds of spin-up.


Of course, real ceiling-fan enthusiasts get around this by using a small solid-fuelled rocket system to do the initial spin-up. Suitably specified, these can produce many megawatts for a small fraction of a second, and also solve the problem of the torque tearing the house off its foundations that the very high torque motors used previously have. Such systems can spin the fan up in tiny fractions of a second, and the achievable rotation rate is really limited only when the tips of the fan blades go supersonic, which tends to destroy the fan. It is best not to be in the room during the spin-up: I believe most people retreat to an underground bunker at least a quarter of a mile away.

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    $\begingroup$ Seems like liquid-fueled rocket engines would be a better choice, since you don't have to replace them with each use. Granted, unless the blades are really strong, you might have to replace them anyway after the blades break and the tips go flying off in various directions. $\endgroup$ – reirab Apr 12 '16 at 16:37
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    $\begingroup$ I've stopped my ceiling fan with my hand numerous times, both by accident and on purpose, without being injured. Probably wouldn't want to do it with the rocket system equipped, though. $\endgroup$ – Random832 Apr 12 '16 at 19:14
  • $\begingroup$ @reirab: the fuel-storage problems turn out to be prohibitive. Attempts were made to run fuel lines down the central bearing of the fan, but leakage (and the resulting fires) were a serious problem. $\endgroup$ – tfb Apr 12 '16 at 21:49
  • $\begingroup$ @tfb Yeah, I was thinking fuel lines running down the fan blades. As a bonus, you shouldn't need a fuel pump, as the fuel should be forced to the outside of the turn, right where you want it. Once the blades are spinning, this should be quite sufficient to pull a vacuum on the lines w/o a pump, assuming they're sealed well. Also, random832 is right. I've stopped ceiling fans with my fingers before, too. It doesn't hurt at all, as long as you do it correctly (i.e. gently from the bottom, like a brake.) Would be more problematic in the rocket-powered version, though. $\endgroup$ – reirab Apr 12 '16 at 21:54
  • $\begingroup$ @reirab You still need pumps to start the engines unfortunately. Yes, the finger thing: I always forget that there are still people who have the old-fashioned subsonic fans. $\endgroup$ – tfb Apr 12 '16 at 22:03
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You might be thinking in comparison to a desk or handheld electric fan.

These things start up quickly!

As mentioned by @Farcher, $\tau = I\alpha$. $I$, the moment of inertia of a spinning body around a particular axis of rotation, is calculated as follows:

$$I = \iiint\rho(x,y,z)||r||^2\ dV$$

Or with uniform density,

$$I = \rho\iiint||r||^2\ dV$$

From this formula, you can see that the moment of inertia of a rotating object increases as its mass is distributed further from the axis of rotation.

I'm going to spare the calculus and look up some formulas in a table so we can verify this easily:

Rod of length $L$ and mass $m$, rotating about its center: $I = \frac{mL^2}{12}$

Rod of length $L$ and mass $m$, rotating about one end: $I = \frac{mL^2}{3}$

Thin circular hoop of radius $r$ and mass $m$: $I = mr^2$

Thin, solid disk of radius $r$ and mass $m$: $I = \frac{mr^2}{2}$

Notice in all of these, the $r$ or $L$ is squared. So since the ceiling fan has longer blades on it than a desk fan does, it'll have a much higher moment, which is responsible for your observation that the $\alpha$ (angular acceleration) is much lower.

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It's a bit complicated (Wikipedia). Induction motors work in sync with the AC frequency but have no torque at 0 RPM so they need some arrangement to get them started. enter image description here

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    $\begingroup$ This only applies to single-phase induction motors. Three-phase induction motors are inherently self-starting. Granted, all ceiling fans have a single-phase motor. $\endgroup$ – ntoskrnl Apr 12 '16 at 15:32
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    $\begingroup$ @ntoskrnl if ceiling fans use a single-phase induction motor, why can't I make them run backwards by just grabbing the blade and pushing it the other way? Am I misunderstanding how these motors work, or is whatever allows it to self-start enough to prevent this? $\endgroup$ – Random832 Apr 12 '16 at 19:17
  • $\begingroup$ @Random832 The latter. Single-phase synchronous motors on the other hand (used to turn the plate in a microwave oven) can run in either direction (if you watch carefully, you'll notice the plate chooses a random direction each time). Induction motors are asynchronous motors by the way, unlike this answer states. $\endgroup$ – ntoskrnl Apr 13 '16 at 14:19
  • $\begingroup$ @ntoskrnl Right, I will delete my answer. The right answer is that brushless motors are quiet, long-lasting and efficient, but have low starting torque. Brush motors (like in a power drill) are noisy and the brushes wear out. You would not want those in your ceiling fan since you don't need fast start-up. This is really an engineering issue, although there might be some fundamental physics reason why you can't make a brushless motor with good starting torque. $\endgroup$ – Keith McClary Apr 13 '16 at 16:18
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When the fan starts spinning, each blade starts from rest. Newton's first law of motion states that unless a force is applied to it, the [velocity][1] of a body does not change. That property is inertia. To speed up, the blades must accelerate. Newton's second law of motion states that the force necessary for an acceleration of a body is proportional to and parallel to the acceleration, and the ratio of the force magnitude to the acceleration magnitude is the mass of the body. Newton's laws of motion describe point particles in linear motion, and the blades are extended bodies in rotational motion. We can understand the blades' motion from Newton's laws, nonetheless.

A (point) particle is a body where all mass is concentrated at one point. It is an idealization, but we can understand real bodies using this concept. An extended body is a body where the mass is spread over a region of space. We can think of the multiple blades of the fan, as several extended bodies, each of which is made up of many particles. When the fan spins, each of the particles moves in a circle.

Consider a single particle. It starts at rest. According to Newton's second law of motion, it will accelerate in the direction of a force applied to it by an amount proportional to the magnitude of the force. The motor applies a force to the particle through the fan blade. If the particle were not attached to the fan blade, it would accelerate in a straight line. The crucial point is that the magnitude of the acceleration is proportional to the force applied. For the fan to reach full speed instaneously, the particle would need to accelerate to full speed instaneously. That is an infinite magnitude acceleration which requires an infinite magnitude force.

The particle is part of the blade, so the blade exerts a force that prevents the particle from moving away from the center of the fan. The result is that the particle accelerates through a very small arc in space in a very small span of time. Then the motor exerts a force on the particle in the new position in a slightly different direction through the blade, and the process repeats. So the particle accelerates in an arc that eventually becomes a circle, and it continues accelerating until it reaches the final speed.

The same process occurs with all of the particles that make up all the blades until all the particles reach their full speed circular motions. Collectively, this process is the process of the fan accelerating in its rotational motion to full speed. Others have explained this more concisely in more technical language. So, the ceiling fan starts slowly because the motor cannot exert an infinite force.

[1]: Velocity is the rate and direction that position changes.

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    $\begingroup$ To me this answer gets closest to something I'm suprised is not in any of the answers so far: The definition of inertia. That's at the heart of the entire question, IMHO. $\endgroup$ – Todd Wilcox Apr 12 '16 at 18:49

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