The radical dimerization of ketones or aldehydes gives vicinal diols through a pinacol coupling reaction. However, the behavior of titanium metals used for the reaction as a source of electrons is unusual. When the reaction is carried out in the presence of titanium, diols can be isolated at low temperatures. Else titanium further reacts with diols, forming alkenes through the McMurry reaction.

Viscous forces, like friction, are intermolecular forces that resist the relative motion of molecules over each other. When a solid body moves through a liquid, viscous forces drag it in the opposite direction. The force's magnitude depends on the solid's shape and size, as well as its speed and the liquid's coefficient of viscosity, density and temperature.
The expression for the force on a solid spherical object in a fluid is called Stokes' law. Stokes' law is valid only for low Reynolds...

In a beam of charged particles created by a heated cathode, the particles move at different speeds. However, many applications need a beam with uniform particle speeds. An arrangement known as a velocity selector uses electric and magnetic fields to pick particles with a particular speed from the beam.
A particle with charge q, speed v, and mass m enters an area from the top, where the magnetic and electric fields are perpendicular both to the particle's motion and to one another. The magnetic...

Mohr's circle is a graphical method to determine an area's principal moments of inertia by plotting the moments and product of inertia on a rectangular coordinate system.

Stone masonry is a construction technique that uses individual stones to build structures and can be categorized into two main types: rubble and ashlar. Rubble masonry uses uneven, naturally shaped stones such as river rocks or fragments from quarries. This method often requires the mason to select and possibly shape each stone to fit the designated space, ensuring a proper build, even with irregular stone sizes and shapes. Ashlar masonry, on the other hand, employs uniformly cut stones that...

When analyzing a bent tube with a circular cross-section subjected to multiple forces, it is crucial to determine the stress distribution in order to maintain structural integrity under varied load conditions.
The process begins by slicing the tube at critical points and analyzing the internal forces and stress components at these sections, focusing on the centroid. Normal stresses, generated by axial forces and bending moments, are either compressive or tensile and vary across the section from...