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A string or rope is often idealized as one dimension, having fixed length but being massless with zero cross section. If there are no bends in the string, as occur with vibrations or pulleys , then tension is a constant along the string, equal to the magnitude of the forces applied by the ends of the string.
The angular deficit δ is linearly related to the string tension (= mass per unit length), i.e. the larger the tension, the steeper the cone. Therefore, δ reaches 2π for a certain critical value of the tension, and the cone degenerates to a cylinder. (In visualizing this setup one has to think of a string with a finite thickness.)
In climbing, a Tyrolean traverse is a technique that enables climbers to cross a void between two fixed points, such as between a headland and a detached rock pillar (e.g. a sea stack), or between two points that enable the climbers to cross over an obstacle such as chasm or ravine, or over a fast moving river. [1]
The rope is on the verge of full sliding, i.e. is the maximum load that one can hold. Smaller loads can be held as well, resulting in a smaller effective contact angle φ {\displaystyle \varphi } . It is important that the line is not rigid, in which case significant force would be lost in the bending of the line tightly around the cylinder.
A slight adjustment can alter it to 100 Hz, exactly one octave above the alternating current frequency in Europe and most countries in Africa and Asia, 50 Hz. In most countries of the Americas—where the AC frequency is 60 Hz—altering A# on the fifth string, first fret from 116.54 Hz to 120 Hz produces a similar effect.
An ant starts to crawl along a taut rubber rope 1 km long at a speed of 1 cm per second (relative to the rubber it is crawling on). At the same time, the rope starts to stretch uniformly at a constant rate of 1 km per second, so that after 1 second it is 2 km long, after 2 seconds it is 3 km long, etc.
Verlet integration (French pronunciation:) is a numerical method used to integrate Newton's equations of motion. [1] It is frequently used to calculate trajectories of particles in molecular dynamics simulations and computer graphics.
Geodesics for massless particles are called "null geodesics", since they lie in a "light cone" or "null cone" of spacetime (the null comes about because their inner product via the metric is equal to 0), massive particles follow "timelike geodesics", and hypothetical particles that travel faster than light known as tachyons follow "spacelike ...