# Jerk

Topics: Velocity, Derivative, Acceleration Pages: 3 (624 words) Published: April 17, 2013
Jerk

• Jerk is the rate of change of acceleration with time.
j =
da

dt
• 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
• The SI unit of jerk is the meter per second cubed.

m/s3
=
m/s2

s

• An alternate unit is the g per second.

g
=
9.80665 m/s2
= 9.80665 m/s3

s

s

• 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 have two otoliths in each ear — 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 οτο (oto, ear) and λιθος (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 "we're accelerating." Since gravity also tugs on the plates, the signal may also mean "this way is down." 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 — 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...