Thursday, August 1, 2019
Jerk (Retrieved from http://physics. info/kinematics-calculus/ ) Ã¢â¬ ¢ Jerk is the rate of change of acceleration with time. j = da dt Ã¢â¬ ¢ Jerk is the first derivative of acceleration, the second derivative of velocity, and the third derivative of displacement. j = da = d2v = d3r dt dt2 dt3 Ã¢â¬ ¢ The SI unit of jerk is the meter per second cubed. ? ? m/s3 = m/s2 ? ? s Ã¢â¬ ¢ An alternate unit is the g per second. ? ? g = 9. 80665 m/s2 = 9. 80665 m/s3 ? ? s s Ã¢â¬ ¢ Why is Jerk a meaningful quantity?The human body is equipped with sensors to sense acceleration and jerk. Located deep inside the ear, integrated into our skulls, lies a series of chambers called the labyrinth. Part of this labyrinth is dedicated to our sense of hearing (the cochlea) and part to our sense of balance (the vestibular system). The vestibular system comes equipped with sensors that detect rotational acceleration (the semicircular canals) and sensors that detect linear acceleration (the otoliths).We h ave two otoliths in each ear Ã¢â¬â one for detecting acceleration in the horizontal plane (the utricle) and one for detecting acceleration in the vertical place (the saccule). Otoliths are our own built in accelerometers. The word otolith comes from the Greek (oto, ear) and (lithos, stone). Each of our four otoliths consists of a hard bone-like plate attached to a mat of sensory fibers. When the head accelerates, the plate shifts to one side, bending the sensory fibers. This sends a signal to the brain saying Ã¢â¬Å"we're accelerating. Since gravity also tugs on the plates, the signal may also mean Ã¢â¬Å"this way is down. Ã¢â¬ The brain is quite good at figuring out the difference between the two interpretations. So good, that we tend to ignore it. (Sight, sound, smell, taste, touch Ã¢â¬â where's balance in this list? ) We ignore it until something changes in an unusual, unexpected, or extreme way. I've never been in orbit or lived on another planet. Gravity always pulls me down in the same way. Standing, walking, sitting, lying Ã¢â¬â it's all quite sedate.Now let's hop in a roller coaster (or engage in a similarly thrilling activity like downhill skiing, Formula One racing, or cycling in Manhattan traffic). Acceleration is directed first one way, then another. You may even experience brief periods of weightlessness or inversion. These kinds of sensations generate intense mental activity, which is why we like doing them. They also sharpen us up and keep us focused during possibly life ending moments, which is why we evolved this sense in the first place.Your ability to sense jerk is vital to your health and well being. Jerk can be both frightening and exciting. Algebraic definition of Jerk: where is acceleration, is velocity, is position, t is time. Jerk is a vector, and there is no generally used term to describe its scalar magnitude (e. g. , Ã¢â¬Å"speedÃ¢â¬ as the scalar magnitude for velocity). The SI units of jerk are metres per second c ubed (metres per second per second per second, m/s3, or mÃ ·s? 3). There is no universal agreement on the symbol for jerk, but j is commonly used.Newton's notation for the derivative of acceleration can also be used, especially when Ã¢â¬Å"surgeÃ¢â¬ or Ã¢â¬Å"lurchÃ¢â¬ is used instead of Ã¢â¬Å"jerkÃ¢â¬ or Ã¢â¬Å"joltÃ¢â¬ . If acceleration can be felt by a body as the force (hence pressure) exerted by the object bringing about the acceleration on the body, jerk can be felt as the change in this pressure. For example a passenger in an accelerating vehicle with zero jerk will feel a constant force from the seat on his or her body; whereas positive jerk will be felt as increasing force on the body, and negative jerk as decreasing force on the body.
Posted by Unknown at 8:38 AM