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While I was looking for the definition of the center of mass , I found this text :
"If a single force acts on a    body and the line of action of the force passes through the centre of mass, the body will have linear    acceleration but possess no angular acceleration."

why does the body have an no angular acceleration if the applied force passes the center of mass ?

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    $\begingroup$ The body has a linear acceleration wherever you push it. That is just Newton's second law of motion. The more interesting question is "why does it have an no angular acceleration if the force passes the center of mass". $\endgroup$ – alephzero Jun 9 '17 at 1:50
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    $\begingroup$ A force is capable of producing both translation i.e displacement along x, y, z axes, as well as rotation or angular displacement. When there exists a distance between the line of action of a force and a point, then there will exist a moment due to the force at that point. Just like net force, if there exists a net moment of force, there will be angular acceleration. Since, in rigid bodies, centre of mass gives us the effect of forces/moments for the entire body, therefore if there is no distance between the line of action of force and the COM of a body, then there will be no angular acc. $\endgroup$ – Mohammad Nayef Jun 10 '17 at 3:41
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That's just a really fancy way of saying "if you push on something right in the center, it will move but won't spin". Are you familar with pool/billiards? If you hit the ball right in the exact center, it will move, but it won't spin. If you hit it a little to the side, or a little above or below center, it will both move and spin.

(of course, the problem with this analogy is that the friction will the table will always cause it to roll as it moves... think of playing billiards in space...)

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  • $\begingroup$ Ford Prefect mentioned a space billiards game where a planet was potted (scored 8 points, but lots died...) ! From The Hitchhikers Guide to the Galaxy. Good answer though. $\endgroup$ – Solar Mike Jun 9 '17 at 4:56

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