An electric motor applies a torque of 700 N·m to an aluminum shaft, triggering a stable rotation. Two pulleys, B and C, are subjected to torques of 300 N·m and 400 N·m, respectively. The modulus of rigidity is provided as 25 GPa. With the knowledge of the length and diameter of each segment, the twist angle between the two pulleys can be computed. First, a section cut is made between pulleys B and C, and the cut cross-section is analyzed using a free-body diagram. Given that the torque...

Consider a cylindrical shaft with a length denoted by L and a consistent cross-sectional radius referred to as r. This shaft undergoes a torque at the free end. The highest shearing strain within the shaft is directly proportional to the twist angle and the radial distance from the shaft axis. When the shaft behaves elastically, this shearing strain can be articulated using variables such as the applied torque, radial distance, the polar moment of inertia, and the modulus of rigidity. By...

Most chemical reactions in cells require enzymes—biological catalysts that speed up the reaction without being consumed or permanently changed. They reduce the activation energy needed to convert the reactants into products. Enzymes are proteins, that usually work by binding to a substrate—a reactant molecule that they act upon.
Enzymes exhibit substrate specificity, meaning that they can only bind to certain substrates. This is mainly determined by the shape and chemical...

Stem cells are undifferentiated cells that divide and produce different types of cells. Ordinarily, cells that have differentiated into a specific cell type are post-mitotic—that is, they no longer divide. However, scientists have found a way to reprogram these mature cells so that they “de-differentiate” and return to an unspecialized, proliferative state. These cells are also pluripotent like embryonic stem cells—able to produce all cell types—and are therefore...

Spontaneous mutations arise infrequently during DNA replication due to errors in the process. A key factor behind these errors is tautomeric shifts in nitrogenous bases, where bases transition from keto to enol forms or amino to imino forms. This shift can alter base-pairing rules, leading to mutations. Additionally, reactive oxygen species (ROS) arising from aerobic metabolism can damage DNA, resulting in depurination (loss of a purine base) or depyrimidination (loss of a pyrimidine base).

A permanent electric dipole orients itself along an external electric field. This rotation can be quantified by defining the potential energy because the external torque does work in rotating it. Then, the potential energy is minimum at the parallel configuration and maximum at the antiparallel configuration. While the former is a stable equilibrium, the latter is an unstable equilibrium.
Since the absolute value of potential energy holds no physical meaning, its zero value can be chosen as per...