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xissburg

about conservation of momentum

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I saw (and also did) an experience that you sit on a chair that can rotate(sorry cuz bad english :)) and someone apply some torque on you and you start rotating. by wide opening and closing your arms you can change your moment of inertia in the axis you're rotating and due to the conservation of angular momentum when you close your arms your moment of inertia diminishes and your angular velocity increases, and when you open your arms your angular velocity diminishes. OK with that, I understand it. But what about the following, a linear case: I'm on a skateboard holding a 20kg sugar package a some velocity v, then I throw the sugar package away. Will the linear momentum be conserved by increasing my linear velocity?! And about this: I'm into a bus at some velocity v. I go near the door to get out the bus but it did not stopped yet and I jump out of it(I often do it. its cool :)). Will the linear momentum be conserved by increasing my velocity?!? I'm not sure if my velocity seems to increase when I jump out of the bus =/ hard to feel. Thanks guys

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The answer is no to both.

The linear situation is different to the angular one, because the body splits into two, each possessing their own momentum. Rather than a moving object changing its moment of inertia (by pulling its legs in), it 'explodes' into two objects, each having their own momentum. A more fitting analogy would be for an object to somehow change its mass without expelling any extra bodies.

The skateboard does not speed up when you leave it, as the momentum doesn't all belong to the skateboard when you step off it - you take some with you. On the other hand, if you jump backwards off the board so that you are stationary (relative to the floor) when you lose contact, then the skateboard will speed up, as is required for conservation of momentum. However, this doesn't seem so special any more, as you give the board a jolt as you are leaving.

The same applies for the bus. If you jump off laterally, then you are taking some momentum with you. On the other hand, if you jump off so that you are stationary upon landing then the bus will accelerate. In a different frame of motion, if you somehow managed to jump forward off the bus with such a force that you stop the bus dead, you will of course come off at a tremendous speed. Good luck with this one [wink].

Admiral

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thanks man ;) now I understand that what is conserved is the momentum of the 'full system'. maybe someday I'll try your last idea, thanks for wishing me luck with that :P

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