We analyze the moment of inertia I(S), relative to the center of gravity, of finite plane lattice sets S. We classify these sets according to their roundness: a set S is rounder than a set T if I(S) < I(T). We show that roundest sets of a given size are strongly convex in the discrete sense. Moreover, we introduce the notion of quasi-discs and show that roundest sets are quasi-discs. We use wea...

Experimental examination of the gyroscopic and rotary inertia effects on the chatter boundary in a milling operation is the chief aim of this article. The equations of motion of the tool vibration are derived based on Timoshenko beam theory and Hamilton principle by considering gyroscopic moment, rotary inertia, velocity-dependent process damping and radial immersion effect. For a range of dept...

We predict an anomaly in highly excited bending spectra of acetylene with high vibrational angular momentum. We interpret this in terms of a vibrational shape effect with moment of inertia backbending, induced by a sequence of bifurcations with a transition from "local" to "orthogonal" modes.

the optimum shape of balance weights is determined, using two different criteria. according to one, one of the balance weights should have minimum size. while the other requires that the mass moment of inertia about the axis of rotation should be minimum. in the second case, the calculus of variation is used to determine the optimum shape. graphs are presented to enable designers to find the di...

the ground state rotational bands of some rare earth nuclei show a rather strange behaviour at large values of angular momenta. the nuclear moment of inertia teta increases smoothly with angular momentum i up to i=12. then at about i=14 there is a sudden increase in the moment of inertia. the plot of teta versus the square of the angular velocity w gives a s-shaped curve. we attempt here to rep...