Install Free Gold Price Widget!
Install Free Gold Price Widget!
Install Free Gold Price Widget!
|
- 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
- Why does a ray parallel to principal axis passes from focus after . . .
A spherical concave mirror does not have a single focus The focal length depends on the point of reflection The point at which a light ray, initially parallel to the principal axis intersects the principal axis is $\textbf{defined}$ to be the focus As the point of reflection approached the center of the lens, the focal length converges to
- Why are the products of inertia zero when an object rotates on a . . .
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 That is why products of inertia are all zero in principle coordinate system
- angular momentum - Principle Axes of inertia and moments of inertia . . .
$\begingroup$ When an object rotates around any general axis, any frame of reference that is fixed on the object (i e whose basis is made of vectors defined on the object) is a rotating frame It is customary to choose the principal axes as a basis, because usually the object is made to rotate around one of them and it makes everything easier
- rotational dynamics - Principal moment of inertia, and principal axis . . .
But I don't know what is the axis of rotation of Ixy, Iyz ,Izx I mean about which axis they are rotating? None Those nonzero off-diagonal terms, if they exist, mean but one thing: That the object in question lacks symmetry (objects with a spherical mass distribution always have a diagonal inertia tensor), and
- How does cutting a biconvex lens in half along its principle axis . . .
We can show that rays parallel to, and not too far from, the axis all converge to a single point on the axis on the other side of the lens – the principal focus – at whatever point on the lens they strike it So either half of the lens (cut as you have shown) will converge the rays to the principal focus
- What happens with an object not originally rotating around its . . .
So, the rotating body wobbles In the absence of friction and external torques, this persists indefinitely However, if the body has internal moving parts subject to friction they may damp the wobble The result is a body rotating around its axis of maximum inertia This is the principle behind "nutation dampers" on spacecraft
- Proof that all rays parallel to the principal axis meet at the focus . . .
This assumes that the the rays are very close to the principal axis See paraxial approximation You have instead used marginal rays in your graphs which are quite far from the principal axis and will thus never converge properly at one fixed point This can be easily fixed by using parabolic mirrors which will by design obey the above rule
|
|
|