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-3

moment is turning effect produced by a force . while torque is due to rotation of body.

1

This is only true for engineering units which have $I$ in ${\rm lbf\,in^2}$. In the metric system the units of $I$ are ${\rm kg\, m^2}$. So to convert force ${\rm lbf}$ to mass you divide by $g$.

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This looks like an example of the Tennis Racket Theorem. Some axes of rotation for a rigid body are more stable than others. If the initial rotation axis does not correspond to one of the principal axes, a wobble can grow and cause the rotation axis to move to a principal axis. This is a result of Euler's Equations of Motion and the moments of inertia. The ...

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Not sure if I am interpreting your description of the problem correctly, but if I take the initial conditions (using nice round numbers) as a rod of $r = 1\:\mathrm{m}$ length, pivoting about one end at at $\omega = 1\:\mathrm{rad/s}$ at $t=0$, I can decompose the motion as a COM motion of $v=r\,\omega/2$ with a spin about the COM of $\omega$. If I plot the ...

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I found the solution. It was much more easier than I believed on first sight. After a good rest on my couch, I saw easily the big deal: The total energy of the system is get by the kinetic energy of the rotating mass $(1/2)Ix_2^2(t)$, that is positive, and the gravitational potential energy $Mgh$, with $h$ obviously pair to $l∗cos(x_1(t))$, that is ...

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