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You have to assume some wacky things for this scenario, but nothing that defies physics as far as I can tell. I'm going to describe this with a human being initially, because I think it makes the scenario clearer, but then I'm going to ask you to replace the human with an appropriate machine.

Let's say I am floating in water, and have an absurdly strong and accurate arm. I also have a screwdriver on my belt. If I threw the screwdriver, conservation of momentum would propel me in water. Now if I threw the screwdriver just fast enough to make it orbit around the Earth and come back to me I would have moved a certain distance before catching the screwdriver. Catching the screwdriver additionally increases my speed. After catching the screwdriver, I should be able to repeat this process. Thus, ignoring relativity for the moment, my speed and distance traveled would increase to infinity. In the human's case, I obviously have to exert energy to throw the screwdriver. What if we replaced the human being with some sort of spring-loaded contraption that did the same thing? Why wouldn't this simply just move forever?

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  • $\begingroup$ If it doesn't defy physics then it isn't considered a perpetual motion machine because those defy physics. $\endgroup$ – Jim May 21 '15 at 16:12
  • $\begingroup$ So where does this defy physics, or alternatively restating the question in my title, why is this not a perpetual motion machine? $\endgroup$ – Dargscisyhp May 21 '15 at 16:17
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    $\begingroup$ A better example might be a satellite orbiting the Earth, with a precisely calibrated cannon. $\endgroup$ – David Z May 21 '15 at 16:22
  • $\begingroup$ @JimtheEnchanter that should be an answer. $\endgroup$ – David Z May 21 '15 at 16:22
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    $\begingroup$ you expend energy throwing and catching, muscles and stuff $\endgroup$ – anna v May 21 '15 at 16:25
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Ignoring many of the limiting factors of this problem (like air and water resistance), this wouldn't do what you think it would because the screw driver would travel around Earth and come back to you from the opposite direction. When you catch it again, it would slow you down again by the same amount that throwing it sped you up. You'd come to a halt.

So let's say you substitute a screw driver (why a screw driver anyway?) for a boomerang so that it comes back from the same direction that you threw it. In this case, you would gain momentum from both throwing and receiving, but that would still not be perpetual motion because there is an input of energy (or rather, momentum) from the air as it is used to reverse the momentum on the boomerang.

Furthermore, as rightly pointed out in the comments by anna v, you yourself are expending energy to throw this object. That means a supply of energy is required from you. Unless you have an infinite store of energy, you can't keep this up in perpetuity. And you can't recover energy from catching the object because that is being used to increase your velocity.

All in all, this doesn't fulfill the requirements to be called a perpetual motion machine. Sorry.

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The answer comes from definition of perpetual motion. In must require no energy input. You however, do use energy by throwing the screwdriver. Eventually, without a source of calories, you will run out of energy.

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