Science in Images: These little-studied mini twisters form beautiful loops under the water's surface
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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...
442
Irrotational flow is characterized by fluid motion where particles do not rotate around their axes, resulting in zero vorticity. For a flow to be irrotational, the curl of the velocity field must be zero. This imposes specific conditions on velocity gradients. For instance, to maintain zero rotation about the z-axis, the gradient condition:
must be satisfied, along with similar conditions for other axes:
A uniform flow, where u is constant and v and w are both zero, satisfies these conditions...
263
Surface tension is a fundamental property of fluids, occurring at the boundary between a liquid and a gas or between two immiscible liquids. This phenomenon arises from the cohesive forces between molecules at the fluid's surface, creating an effect similar to a stretched elastic membrane. Inside each fluid, molecules are equally attracted in all directions by neighboring molecules, but surface molecules experience a net inward force, resulting in surface tension.
Surface tension varies...
285
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...
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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...
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A wave is a disturbance that propagates from its source, repeating itself periodically, and is typically associated with simple harmonic motion. Mechanical waves are governed by Newton's laws and require a medium to travel. A medium is a substance in which a mechanical wave propagates, and the medium produces an elastic restoring force when it is deformed.
Water waves, sound waves, and seismic waves are some examples of mechanical waves. For water waves, the wave propagation medium is...