A new RING tossed into an old HAT

One of the distinctive characteristics of circular shafts is their ability to maintain their cross-sectional integrity under torsion. In other words, each cross-section continues to exist as a flat, unaltered entity, simply rotating like a solid, rigid slab. To understand the distribution of shearing stress within such a shaft, consider a cylindrical section inside this circular shaft. This section has a length of L and a radius of R, with one end fixed. The radius of the cylindrical section is...

A toroid is a closely wound donut-shaped coil constructed using a single conducting wire. In general, it is assumed that a toriod consists of multiple circular loops perpendicular to its axis.
When connected to a supply, the magnetic field generated in the toroid has field lines circular and concentric to its axis. Conventionally, the direction of this magnetic field is expressed using the right-hand rule. If the fingers of the right hand curl in the current direction, the thumb points in the...

Contractile rings are composed of microfilaments and are responsible for separating the daughter cells during cytokinesis. Contractile ring assembly proceeds along with other cell cycle events; however, very few mechanistic details are known about the timing and coordination of the contractile rings with the cell cycle.
A small GTPase, RhoA, controls the function and assembly of the contractile ring. RhoA belongs to the Ras superfamily of proteins. The activation of formins by RhoA promotes...

Contractile rings are composed of microfilaments and are responsible for separating the daughter cells during cytokinesis. Contractile ring assembly proceeds along with other cell cycle events; however, very few mechanistic details are known about the timing and coordination of the contractile rings with the cell cycle.
A small GTPase, RhoA, controls the function and assembly of the contractile ring. RhoA belongs to the Ras superfamily of proteins. The activation of formins by RhoA promotes...

A torsional pendulum involves the oscillation of a rigid body in which the restoring force is provided by the torsion in the string from which the rigid body is suspended. Ideally, the string should be massless; practically, its mass is much smaller than the rigid body's mass and is neglected.
As long as the rigid body's angular displacement is small, its oscillation can be modeled as a linear angular oscillation. The amplitude of the oscillation is an angle. The role of mass is played by the...

Circular shafts undergoing torsional stress maintain their cross-sectional integrity due to their axisymmetric nature. This symmetry ensures an even distribution of stress, allowing the shaft to withstand torsion without distorting. In contrast, square bars, lacking this axial symmetry, experience significant distortion across their cross-sections when subjected to torsion, with the exception of along their diagonals and at lines connecting midpoints. A detailed examination of a cubic element...