I have this conceptual doubt which might be flawed very badly but I don't understand this particular thing. For example, if one end of a stick is moving with velocity $v_1$ and the other with $v_2$, how do I enter the frame of the stick?
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$\begingroup$ What does "the frame of the stick" mean? $\endgroup$– WillOCommented Apr 27 at 14:22
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$\begingroup$ The frame of the stick is the frame in which the centre of mass of the stick is stationary i.e. the total linear momentum of the stick is zero. If v₁ ≠ v₂ the stick will be rotating in about its centre of mass in this frame. $\endgroup$– John RennieCommented Apr 27 at 15:18
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$\begingroup$ @WillO that is my doubt. $\endgroup$– Krave37Commented Apr 29 at 4:40
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$\begingroup$ @JohnRennie is this a defination, because in my book the author uses the frame of the stick, and says that fly moves with constant velocity in the frame of the stick $\endgroup$– Krave37Commented Apr 29 at 4:41
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1$\begingroup$ @Krave37 Four decades of doing physics :-) $\endgroup$– John RennieCommented Apr 29 at 8:13
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1 Answer
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You choose a point of the rigid body to work with. This is most often the center of mass (which offers some additional nice properties) but need not be. Chasles' theorem states that if you pick a point $p$ of any rigid body, the instantaneous motion of the body is the sum of the translational motion of $p$ and rotation about an axis passing through $p$. The reason this can be done is the definition of rigid body, which mandates that the distance between any two points is fixed.
answered Apr 27 at 9:17
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$\begingroup$ I was thinking what if, I break the motion into two parts, One along the stick, and the other perperdicular. If I enter the frame of a person moving along the stick witht he same speed, then will I see the stick rotating about a fixed axis? Also, the original question was that a fly is on a stick and as the stick moves with different velocities at its ends, the fly moves with a constant velocity relative to the stick. What does this mean? $\endgroup$– Krave37Commented Apr 29 at 4:40
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1$\begingroup$ @Krave37 In general, no. The axis can vary with time. All this is saying is that if you choose a point on the object and enter the frame of that point, the object will be purely rotating. $\endgroup$ Commented Apr 29 at 6:24