Why do your arms feel tired when you hold them in the air parallel to the ground?

In your system, you are correct. The only force you are exerting, is to overcome the Gravitational force. I would argue, however, that this is not small. The one part of the equation you are missing is the lever action of your arm. The weight of your arm (Gravitational force toward the earth) is exerting a force on your shoulder, primarily. The actual mathematics would require some calculus, but taking some assumptions will simplify the math and show my argument. Assume: Arm length = 3 ft Arm is weightless, with the exception of the Hand. The Hand weighs 1lb. Gravity acts perpendicular to the ground (90 Degrees) The force which the shoulder will have to exert in order to make up for the gravitational force exerted on the Hand (the Weight of the Hand) is rotational, therefore a torque. The calculation is as follows: <Torque> = <Weight of the Hand> X sin (angle at which force is applied) X <Distance from pivot> Plug in... <Torque> = 1lb X 3 ft X Sin (90 Degrees) => 3 ft-lb of torque. This means that your hand is exerting a torque on your shoulders THREE TIMES AS MUCH as it weighs. When you take into account the added weight of the rest of your arm, with the muscles, bone, skin, clothing, wristwatch, etc. (Also accounting for the shrinking lever action as you get closer to the shoulder), the total force you must exert to overcome the 'small gravitational potential energy' isn't so small, after all. Having established that the gravitational force is not slight, your question looks into why the arm feels tired. As mentioned in an earlier answer, THAT comes from Physiology. Most of the energy in your body comes from the oxidation of a Carbohydrate, or sugar. This is done through respiration, which can be anaerobic or aerobic. Aerobic Respiration: Sugars (C6 H12 O6) react with oxygen (O2) to produce Carbon Dioxide (C O2) and water (H2 O). This is the reaction that occurs when there is enough oxygen present in the area. The stored oxygen in your blood is used during the first period of exertion. In your case, the first few seconds to a minute. Once that oxygen store is depleted, you get... Anaerobic Respiration: Sugars (C6 H12 O6) are broken down into two Lactic Acid molecules (C3 H6 O3). This Lactic Acid is what causes the burning/aching feeling of your muscles. Anaerobic Respiration occurs when there isn't enough oxygen to support Aerobic Respiration. This generally occurs after extended exertion. In your case, after that first minute. This buildup of Lactic Acid, over time, creates something known as the 'Oxygen Debt'. After you have relaxed your arms, and you are no longer in need of more energy, your body stops breaking down the carbohydrates into Lactic Acid. However, the Lactic Acid still in your body must be disposed of. After you begin an excessive, your breathing quickens. This is the body attempting to increase it's oxygen intake. When you stop exercising, your breathing takes a few minutes to return to normal. This is because the body is paying back that 'Oxygen Debt'. By continuing to take in more oxygen then is normally needed, the body is able to oxidize the Lactic Acid that built up into Water and Carbon Dioxide. As the Lactic Acid is oxidized, the demand for oxygen decreases, your breathing slows, and your muscles stop to ache as much. Your 'Debt' is repaid. Now, this Lactic Acid causes some amount of damage to your muscles, which your body must repair. This is why the ache can return an hour after the exercise, and also why such activities strengthen your muscles. They are repaired better, stronger, and more resilient, provided the initial damage is not too great. No pain, no gain, perhaps...but you CAN overexert yourself, and cause excessive damage to your muscles.

Huh? Lol, your logic doesn't make sense. First of all, if what you said were true in terms of simply keeping one's arms in the air, the person holding them wouldn't feel tired in the first place. Let me explain further: The fatigue experienced from simply holding one's arms in the air comes from the amount of energy that is internally being expended by the body. Your body takes in oxygen and glucose (from food) which is then chemically turned to energy (ATP), carbon dioxide, and water (If you don't believe the water part, just try exhaling in the cup of your hands for a few moments. They'll be moist in a matter of seconds). Anyway, because the amount of energy you expend is dependent upon the amount of oxygen and glucose you intake (and considering for the moment of simply holding up your arms, it's directly dependent upon just the frequency at which you're respirating, i.e., breathing), the more excessively you repsirate (breathe), the more energy you'll be producing which allows for a more efficient contraction of muscle which govern the movement of your bone structure. In shorter terms, the reason why you feel fatigued after a while is, assuming that you've been respirating at a constant rate, and that you've not taken in any food, the amount of oxygen your body needs to continue contracting your muscles for your arms to remain held in place increases. A build up of lactic acid may occur such that you're placing yourself under a condition where the rate of energy demand by tissues cannot be met by aerobic respiration i.e. tissues cannot get or process oxygen and substrates quickly enough. This is how holding up your arms (long enough) is thought to be even painful by the subject. Get the difference? Not much has to deal with the direct laws of physics in this instance. Think biology in cases of the body--especially on an internal level.

The weight of gravity and harder for blood to flow?