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Why can't we use conservation of linear momentum when an impulse is given to a free rigid body (e.g. at one end of the rod) and the rod is set into general rigid body motion (translation plus rotation)?

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    $\begingroup$ @WrichikBasuIndian 's comment is very mistaken. 1) you cannot sum quantities of different units (such as linear and angular momentum); and 2) if there's an impulse, momentum isn't conserved -- see WAH's answer bellow. $\endgroup$ – stafusa Jul 30 '17 at 23:44
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An impulse by definition changes the linear momentum. Define the impulse as $I$. Then $I\equiv F_{avg}\Delta t=\Delta p=p_f-p_i$. If $I\ne0$ then $\Delta p\ne0$ and $p_f\ne p_i$, which is to say that linear momentum isn't conserved.

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