When it comes to studying the behavior of objects in mechanics, one of the most important tools available is the free-body diagram. Consider a simple example of a system of two blocks coupled by a massless string over a frictionless pulley. Block 1 is sliding over a table pulled by block 2 as block 2 falls under gravity.
To find the acceleration of the system, it is first necessary to calculate the net force on the system. In order to accomplish this, a free-body diagram can be created to...

Chemical reactions often occur in a stepwise fashion involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs. Each of the steps in a reaction mechanism is called an elementary reaction. These...

Deoxyribonucleic acid, or DNA, is the genetic material responsible for passing traits from generation to generation in all organisms and most viruses. DNA is composed of two strands of nucleotides that wind around each other to form a spring-like structure called a double helix. However, the double helix is not perfectly symmetrical. Instead, there are regularly occurring grooves in the structure. The major groove occurs where the sugar-phosphate backbones are relatively far apart. This space...

Overview

The second law of thermodynamics can be stated in several different ways, and all of them can be shown to imply the others. The Clausius’ statement of the second law of thermodynamics is based on the irreversibility of spontaneous heat flow. It states that heat will not flow from the colder body to the hotter body unless some other process is involved. Additionally, as per the Kelvin’s statement, it is impossible to convert the heat from a single source into work without any other effect. This...

The perpendicular-axis theorem states that the moment of inertia of a planar object about an axis perpendicular to its plane is equal to the sum of the moments of inertia about two mutually perpendicular concurrent axes lying in the plane of the body.
Consider a circular disc of mass M and radius R lying along an x-y plane. The origin lies at the center of the disc, and the z-axis is perpendicular to the disc's plane. All three axes coincide at the disc's center. The moment of inertia of this...