What is the physical meaning of the principal axes of inertia?
One way to say it: you do not need to apply any external torque to keep an object rotating about a principal axis. To maintain constant angular velocity around any axis through the center of mass which cannot be defined as a principle axis, torque is required. Consider an ideal barbell, with equal point masses separated by a massless rod.
rotational dynamics - Principal moment of inertia, and principal …
I have read about moment of inertia in rotational mechanics, and also read about moment of inertia tensor where 9 components are present where Ixx, Iyy, Izz are diagonal elements of moment of inertia
The principal axis of a flat object - Physics Stack Exchange
2024年1月20日 · $\begingroup$ A vertical (parallel to z axis) passing through the COM is one of the axis of inertia, due to the symmetry of the object. For a generic shape, there are only 2 orthogonal eingenvectors in the xy plane.
Principal axis of inertia - Physics Stack Exchange
2017年4月4日 · Principal axis of inertia u is a unit vector along a principal axis if I . u is parallel to u There are 3 independent principal axes! I have these questions about it: What is an axis of inertia?
Principal axes of a rigid body - Physics Forums
2010年4月19日 · Hi Amith2006! "The" principal axes are defined as going through the centre of mass. But if a body is constrained to pivot about a fixed point other than the centre of mass, then its angular momentum will still be parallel to its angular velocity if the angular velocity is parallel to a principal axis.
Why are the principal axes about the center of mass of a cube ...
2014年12月15日 · So the principal moments of inertia are all 1 (1 is an eigenvalue of multiplicity 3). When you attempt to calculate the eigenvectors to identify the principal axes, the result is that every vector is an eigenvector of the identity matrix, which is expected.
Rotation about a principal axis, zero torque and all that
2021年10月26日 · $\begingroup$ "For a rotation around a principal axis ωˆ , the lack of need for any torque means that if the object is pivoted at the origin, and if the origin is the only place where any force is applied (which implies that there is zero torque around it), then the object can undergo rotation with constant angular velocity ω. If you try to ...
What is the physical significance of the off-diagonal moment of …
This is equivalent to writing your MOI in a basis where the rotation axis is one of the basis vectors, in which case there are off-diagonal elements, which is what your question is asking about. So, off-diagonal elements in your MOI are equivalent to having a rotation axis that is not aligned with any of the principal axes. Again, this only ...
mathematically, what exactly is the principal axis of a lens?
2022年11月1日 · $\begingroup$ In elementary work (and quite possibly in more advanced treatments) the principal axis is the straight line passing through the centres of curvature of the two lens faces. This line is unaffected by cutting bits out of the lens. $\endgroup$
Why are the products of inertia zero when an object rotates on a ...
2017年11月19日 · Products of inertia are roughly the measure of how rotating around one axis can give angular momentum with respect to another axis. The principle coordinate system is the one for which the angular momenta are decoupled, in the sense that rotating around one axis yields only angular momentum around that axis.