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I know that we can rotate a deformable object using internal forces only in space. Thus we can cause an angular displacement without the use of any external forces.

The following youtube video shows are real life example to do so - http://www.youtube.com/watch?v=RtWbpyjJqrU

My question is

Can we do the same with linear motion also? By that I mean, can we cause a displacement in an object using only internal forces. I could not think of such a setup. And if we can what makes the angular displacement more special than linear displacement?

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We can rotate an object using internal forces only? I think something inside the object must then rotate in an opposite too, otherwise the conservation of angular momentum would be violated. –  namehere Dec 5 '12 at 9:55
Yes, but did u see the video link that I gave? It explains how. –  Tushar Mathur Dec 5 '12 at 10:03
@namehere No, it does not violate conservation of angular momentum to have net angular displacement. See physics.stackexchange.com/questions/10720/… –  Mark Eichenlaub Dec 5 '12 at 10:03
Oops. I misunderstood the question. Obviously I didn't watch the video. I thought OP meant the object ended with a net angular velocity. –  namehere Dec 5 '12 at 10:06

3 Answers 3

up vote 1 down vote accepted

No. Momentum is conserved. Since momentum is mass times the velocity of the center of mass, if the momentum is zero, the center of mass can't move. Alternately, if the center of mass is already moving, it will keep moving indefinitely in a straight line when there are no external forces.

However, in curved spacetime the above may not hold. See http://dspace.mit.edu/handle/1721.1/6706

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But we are able to get angular displacement using only internal force as per the video link. What makes the linear motion so special? –  Tushar Mathur Dec 5 '12 at 10:03
I believe I already answered that. You can integrate linear momentum to get displacement of the center of mass. You cannot integrate angular momentum to get an angular displacement because the moment of inertia can change. –  Mark Eichenlaub Dec 5 '12 at 10:07
Thanks, I get it now. –  Tushar Mathur Dec 5 '12 at 10:10

I was thinking about this and came up with an answer that seems as if you can, so I post it merely as food for thought. In free space I believe the answer is no (Newtons 3rd law). But if you were to stand on a cart or skateboard you can, by touching nothing else (ground/walls etc) scoot yourself forward or backward with a special motion. As far as I can summize from experience, this wouldn't work in a friction-less environment. You might then say there is technically an external force acting but it is induced specifically because one converts gravitational potential energy into kinetic by lowering and raising their center of mass. The special scoot is posible due to friction.

Compare and contrast this scenario to that of one where a person stands on a skateboard with a rope attached to the front and tries to move forward by pulling on the rope. Impossible.

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First of all in your first sentence you are saying that we can rotate a deform-able body without any external force.This is not true because in the absence of external force the net torque on the body will be zero and angular momentum of the body will be conserved and that can be interpreted as you can only increase its angular velocity.So if it is not rotating at all you can never rotate it.

The same reasoning is true for displacement and here momentum is conserved.

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