Rickets: Twists and turns in the Gordian knot

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...

Tension is a force along the length of a medium, in particular, a force carried by a flexible medium, such as a rope or cable. The word "tension" comes from Latin, meaning "to stretch". Not coincidentally, the flexible cords that carry muscle forces to other parts of the body are called tendons. Any flexible connector, such as a string, rope, chain, wire, or cable, can exert pull only parallel to its length; so, a force carried by a flexible connector is a tension with a direction parallel to...

Tension is a force along the length of a medium, in particular, a force carried by a flexible medium, such as a rope or cable. The word "tension" comes from Latin, meaning "to stretch". Not coincidentally, the flexible cords that carry muscle forces to other parts of the body are called tendons. Any flexible connector, such as a string, rope, chain, wire, or cable, can exert pull only parallel to its length; so, a force carried by a flexible connector is a tension with a direction parallel to...

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 exerted...

Rigidity and myotonia are distinct abnormalities of muscle tone that affect resistance and relaxation during movement. Although both involve altered muscle contraction, they arise from different neurological and muscular mechanisms.CharacteristicsRigidity is characterized by uniform resistance to passive movement across the entire range, independent of speed, affecting flexors and extensors equally. It may appear as lead-pipe rigidity (smooth, constant resistance) or cogwheel rigidity...

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...