Thursday, 7 May 2020

torque - Component of angular momentum perpendicular to the rotation axis in rigid body rotation



I have difficulties in understanding, in the rotation of a rigid body, the properties of the component of the angular momentum vector L which is perpendicular to the fixed axis of rotation z. I will call this component Ln. Suppose that the angular velocity Ω is constant in direction but can vary in magnitude.


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|Ln,i|=miriRiΩcosθi|Ln|=ΩmiriRicosθi


Can I therefore say that |Ln||Ω| (1)?


If so, suppose to apply a torque perpendicular to the z axis and parallel to Ln, so that the magnitude of this vector increases. Follows from (1) that there should be an angular acceleration α, although we are in the absence of a torque with an axial component.


This would go against the fact that Izα=Mz (Where Iz is the moment of inertia with respect to the z axis and Mz is the axial component of the exerted torque).




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