How a Gyroscope Works ⚡ What a Gyroscope Is
Summary
TLDRThis video script delves into the workings of gyroscopes, devices that measure orientation and angular velocity. It covers mechanical gyroscopes, which rely on Newton's laws and the concept of precession, to determine orientation and speed. The script also explores the Coriolis effect in vibrating gyroscopes, used in smartphones for their compact size and low cost, despite their sensitivity to linear accelerations. Finally, it introduces optical gyroscopes, which leverage the Sagnac effect for high accuracy and are now miniaturized, illustrating the evolution and applications of gyroscopes in various fields.
Takeaways
- 🌀 A gyroscope can measure either the orientation change or the angular velocity of a system relative to a reference axis.
- 📱 Gyroscopes are used in various applications including smartphones, aeronautics, video games, and robotics, and the human body has a natural gyroscope in the form of the vestibular system.
- 🔧 Mechanical gyroscopes work on the principles of torque and angular momentum, and their operation can be understood through Newton's laws of motion.
- 🎯 The spatial rigidity of a rotating object allows a gyroscope to maintain its orientation even when the rest of the system rotates, which was historically used for navigation.
- 🚴 Precession, a circular motion resulting from a force applied to a rotating object, is used in mechanical gyroscopes to determine the angular velocity of a system.
- 🏗️ The limitations of mechanical gyroscopes include their size and sensitivity to the moment of inertia of the rotating mass, which affects their accuracy and usability.
- 🌊 Coriolis effect gyroscopes are widely used due to their small size and low cost, making them suitable for integration into electronic devices like smartphones.
- 🔄 Coriolis acceleration is a key principle in vibrating gyroscopes, which can calculate angular velocity based on the force experienced by an oscillating mass.
- 🚫 Vibrating gyroscopes can be affected by linear accelerations, which may compromise their accuracy if the system is exposed to large accelerations.
- 💡 Optical gyroscopes operate based on the Sagnac effect, where the difference in distance traveled by light beams in opposite directions within a rotating system allows for the calculation of angular velocity.
- 🔬 Optical gyroscopes offer high accuracy and reliability, with no moving parts, and have been miniaturized to as small as 2 millimeters square in recent advancements.
Q & A
What are the two primary functions of a gyroscope?
-A gyroscope can provide information about the variation of the orientation of a system with respect to a reference axis and provide information about the rate at which the orientation of a system varies when it is rotating, which is its angular velocity.
In what applications are gyroscopes commonly used?
-Gyroscopes are used in a wide range of applications including smartphones, aeronautics, video game consoles, and robotics.
What is the human body's built-in gyroscope known as?
-The human body has a built-in gyroscope known as the vestibular system, which provides information about our orientation and helps us maintain balance.
What are the two factors that determine angular momentum in a rotating system?
-Angular momentum is determined by the moment of inertia of the system, which depends on its shape and mass distribution, and the angular velocity, which indicates how many degrees the system rotates during a defined period of time.
How does the spatial rigidity of a rotating object relate to the operation of a mechanical gyroscope?
-The spatial rigidity of a rotating object means that if a disk is rotating at a certain angular velocity and there are no other forces generating torque, its angular momentum will be conserved, allowing it to maintain its orientation even if the rest of the system moves.
What is precession and how is it used in mechanical gyroscopes?
-Precession is a circular motion generated when a rotating object is affected by a force that causes it to change its orientation. In mechanical gyroscopes, precession is used to determine the speed of a system by measuring the torque generated on a torsion bar when the system is rotated about an axis.
What is the limitation of mechanical gyroscopes in terms of size and accuracy?
-Mechanical gyroscopes' operation depends on the moment of inertia of the rotating disc, which is related to its mass. Therefore, it is impossible to reduce the size of these systems without affecting their accuracy or rotation time.
What is the principle behind the operation of a Coriolis effect vibrating gyroscope?
-Coriolis effect vibrating gyroscopes operate based on the Coriolis acceleration, which occurs when an oscillating mass experiences a force due to the system's rotation, causing it to move laterally. This displacement can be measured to calculate the angular velocity of the system.
How do optical gyroscopes detect angular velocities independent of linear accelerations?
-Optical gyroscopes work on the Sagnac effect, where two beams of light travel in opposite directions in a fiber optic ring. The difference in the distance traveled by the light beams due to the system's rotation allows for the calculation of angular velocity, independent of linear accelerations.
What is the advantage of optical gyroscopes over mechanical and Coriolis effect vibrating gyroscopes in terms of operation?
-Optical gyroscopes have the advantage of being highly accurate and reliable, as they can operate without moving parts. They are also not affected by linear accelerations, which can compromise the accuracy of mechanical and Coriolis effect vibrating gyroscopes.
What was a significant development in the size of optical gyroscopes in 2018?
-In 2018, scientists at Caltech were able to build an optical gyroscope that was just two millimeters square, showing that size is no longer a limitation for these types of gyroscopes.
Outlines
🌌 Gyroscopes: Orientation and Angular Velocity Detectors
This paragraph introduces gyroscopes, devices that measure orientation changes or angular velocity. They are used in various applications such as smartphones, aeronautics, and robotics. The human vestibular system is highlighted as a natural gyroscope that helps maintain balance. The video will explore different types of gyroscopes, starting with mechanical ones, which rely on torque and angular momentum concepts. The paragraph explains the principles of torque and angular momentum in rotating systems and how they relate to Newton's laws of motion. It also discusses the historical use of mechanical gyroscopes for orientation and their application in modern technology, such as the Gravity Probe B satellite.
🔄 Understanding Precession in Mechanical Gyroscopes
The second paragraph delves into the concept of precession, a phenomenon where a rotating object subjected to a force perpendicular to its axis of rotation changes orientation. It explains how precession can be used to determine the angular velocity of a system. The paragraph describes a mechanical gyroscope system with a rotating disc suspended by torsion bars that can measure angular velocity by detecting the torque applied to the system. It also touches on the limitations of mechanical gyroscopes, such as the dependence on the moment of inertia and the challenges of miniaturization without affecting accuracy.
📳 Coriolis Effect and Vibrating Gyroscopes
This paragraph discusses the Coriolis effect vibrating gyroscope, a widely used type due to its small size and low cost, making it suitable for integration into electronic devices like smartphones. It explains the principle of operation based on the Coriolis acceleration, which occurs when a particle moves radially in a rotating system. The paragraph describes how the displacement of an oscillating mass due to the Coriolis force can be measured to calculate the system's angular velocity. However, it also notes the disadvantage of these gyroscopes, which is their susceptibility to inaccuracies when exposed to large linear accelerations.
🌐 Optical Gyroscopes and the Sagnac Effect
The final paragraph introduces optical gyroscopes, which operate based on the Sagnac effect. It describes how two beams of light traveling in opposite directions in a fiber optic ring can be used to measure angular velocity. The difference in distance traveled by the beams due to the system's rotation results in a phase difference, which can be measured to calculate the angular velocity. Optical gyroscopes are highlighted for their high accuracy and reliability, as they have no moving parts. The paragraph also mentions the recent advancements in miniaturizing optical gyroscopes, citing an example from Caltech.
Mindmap
Keywords
💡Gyroscope
💡Angular Velocity
💡Torque
💡Angular Momentum
💡Moment of Inertia
💡Precession
💡Coriolis Effect
💡Sagnac Effect
💡Optical Gyroscope
💡Vestibular System
Highlights
A gyroscope provides information about orientation variation or angular velocity in rotating systems.
Gyroscopes are used in phones, aeronautics, video game consoles, and robotics.
The human body has a built-in gyroscope called the vestibular system for balance and orientation.
Torque and angular momentum are fundamental to understanding gyroscope operation.
Mechanical gyroscopes rely on the spatial rigidity of rotating objects to maintain orientation.
Leon Foucault's gyroscope used a high-speed spinning disc to demonstrate orientation independence from Earth's rotation.
Precession is a key phenomenon for mechanical gyroscopes to determine angular velocity.
Torsion bars in mechanical gyroscopes allow measuring angular velocity through resistance to torque.
Coriolis effect vibrating gyroscopes are widely used in small electronic devices due to their compact size and low cost.
Coriolis acceleration is utilized in vibrating gyroscopes to calculate angular velocity based on mass displacement.
Linear accelerations can affect the accuracy of vibrating gyroscopes, necessitating alternative types.
Optical gyroscopes operate based on the Sagnac effect, detecting angular velocities without being influenced by linear accelerations.
The Sagnac effect involves light beams traveling in opposite directions in a fiber optic ring, with differences in path length affecting their interference.
Optical gyroscopes are highly accurate and reliable, with no moving parts.
Advancements have allowed the miniaturization of optical gyroscopes to just 2 millimeters square.
The video provides an in-depth look at the working principles of different types of gyroscopes and their applications.
Transcripts
a gyroscope is a device that depending
on its composition can fulfill two
functions to provide information about
the variation of the orientation of a
system with respect to a reference axis
or to provide information about the rate
at which the orientation of a system
varies when it is rotating that is its
angular velocity
gyroscopes are used in a wide range of
applications including our phones
aeronautics video game consoles and
robotics
moreover our own body has a built-in
gyroscope known as the vestibular system
which gives us information about our
orientation and helps us maintain our
balance
that is why in this video we will see
how a gyroscope works including
mechanical coriolis effect vibratory and
optical gyroscopes
let's start by looking at how mechanical
gyroscopes work and to do that we need
to understand what torque and angular
momentum are
in a system with an axis of rotation
when we apply a force at a point away
from the axis a torque is generated
which rotates the system and is
represented as a vector parallel to the
axis of rotation
in addition to this when a system is
rotating it has an angular momentum as
well which is also represented by a
vector parallel to the axis of rotation
and is determined by two factors
first the moment of inertia of the
system which depends on its shape and
mass distribution and second the angular
velocity which tells us how many degrees
the system rotates during a defined
period of time
understanding this we can rely on the
operation of an accelerometer to
understand the operation of this first
type of gyroscope
in the previous video we saw how some of
newton's laws could be used to know the
linear acceleration of a system
newton's first law tells us that when
the net force applied on an object is
equal to 0 its acceleration is also zero
and consequently its velocity will
remain constant
similarly if we have a system which is
capable of rotating on an axis and the
net external torque acting on it is zero
the total angular momentum of the system
will also remain constant
on the other hand newton's second law
tells us that the force applied on an
object is equal to its mass multiplied
by the acceleration generated as a
result of the applied force
similarly for rotating systems the
torque of the net force acting on a
system is equal to the rate of change of
its angular momentum which in this case
is also equal to the moment of inertia
multiplied by the angular acceleration
having clarified this we can finally
focus on the practical applications of
these principles in mechanical
gyroscopes
the first application makes use of the
spatial rigidity of a rotating object if
we rotate a disk at a certain angular
velocity and there are no other forces
that generate any torque on the disc its
angular momentum will be conserved
because of this it will continue to
rotate on the same axis and therefore
maintain its orientation this was used
by leon foucault who mounted a disc on a
card and suspension or gimbal which
allows free rotation of the centerpiece
in this system by rolling the center
disc at a high speed or in technical
terms applying a large angular momentum
to it its orientation will not change
even if the rest of the system does
in ancient times when gps did not exist
they were extremely useful as an
alternative method of orientation
because unlike compasses which use the
magnetic fields of the planet to orient
themselves and indicate north this type
of gyroscope could be oriented in any
direction desired and its accuracy would
not be affected by variations in
magnetic fields
although of course its limitation is
that the friction of the axis however
small would eventually reduce the
angular momentum of the disk and
similarly the torque transmitted by the
suspension however small would
eventually change the original
orientation anyway in spite of all this
it is still a valid method for
particular cases at present
an example of this is gravity probe b a
satellite used to test albert einstein's
theory of relativity and whose
gyroscopes could theoretically rotate
for up to fifteen thousand years which
by the way is extremely complex and a
perfect subject for a future video
now going back to the topic the second
practical application of mechanical
gyroscopes is to determine the speed of
a system and to do this they take
advantage of a physical phenomenon
called precession
in simple terms precession is a circular
motion that is generated when a rotating
object is affected by a force that
causes it to change its orientation an
example of this would be a bicycle wheel
hanging at one end of its axle which if
it were at rest would fall due to
gravity
however by possessing an angular
velocity this counter-intuitive
phenomenon known as precession occurs
first it is able to stay in its original
orientation without falling and second
it begins to rotate around the
supporting point
to understand why precession occurs
let's take a closer look at what happens
to the wheel
respect to its supporting point the
weight will generate a perpendicular
torque that would cause the wheel to
fall to the ground however according to
the second law the torque will generate
a small change of angular momentum in
its direction which in this case has no
vertical component by adding the initial
angular momentum with the small change
due to the torque the resulting angular
momentum and thus the wheel's axis of
rotation will have slightly changed its
orientation horizontally without falling
due to gravity moreover since it is
always true that the torque generated by
the weight will be perpendicular to the
angular momentum of the wheel then the
wheel will roll continuously forming a
circumference this relationship between
the torque applied to a rotating object
and the rotation resulting from
precession is what we can use to
determine the angular velocity of a
system
more specifically we can have a system
like this with a rotating disc at the
center which in turn will be suspended
by torsion bars
these will allow the suspension
supporting the disc to rotate but will
also impose a resistance that will
increase proportionally to the torque
which means they allow us to use the
angle of torsion to calculate the
applied torque similar to how springs
allow us to use elongation to calculate
the applied force
this particular system is made to detect
movements in the z-axis
if the central disk is rotating and the
whole system is rotated about the z-axis
the precession will generate a torque on
the torsion bar and the frame will
rotate slightly marking a value on a
conversion scale allowing the angular
velocity of the system to be known
it's not the most intuitive system in
the world but that makes it even more
impressive from a design standpoint
in addition these systems have one major
limitation since their operation
originally depends on the moment of
inertia of the rotating disc which as i
mentioned at the beginning depends on
the mass of the disc it is impossible to
reduce the size of these systems without
affecting their accuracy or rotation
time but we had to start from something
the next type of gyroscope we will
discuss is the coriolis effect vibrating
gyroscope
this type of gyroscope is one of the
most widely used nowadays as they can be
manufactured in really small sizes at a
low cost and therefore can be integrated
into all kinds of electronic devices
such as your phones
to understand the principle of their
operation we must understand what
coriolis acceleration is
imagine a particle rotating around a
point at a constant angular velocity
the particle's trajectory will form a
circle with a radius r1 and the particle
will have a tangential velocity of one
now if that particle moves radially to a
distance t2 the size of the circle
defining its trajectory will increase
and therefore its tangential velocity
will also have to increase to continue
rotating at the same angular velocity
in other words if the tangential
velocity increases then there is an
acceleration which is known as coriolis
acceleration in honor of its discover
this acceleration by the way can be
calculated as minus two times the
angular velocity of the particle
multiplied by the speed at which it
moves radially values that we can then
replace in the classic formula of force
equals mass times acceleration
thus if we have a system in which we
know the value of the mass the velocity
perpendicular to the axis of rotation
and the applied force we can calculate
its angular velocity
an example of a device with such
characteristics would look something
like this in this configuration a mass
is forced to oscillate with a frequency
of several kilohertz
because of this when the system has been
rotated the oscillating mass will
experience a coriolis force that will
move it to the left or to the right
depending on the direction of the
vibration
and similar to accelerometers this
displacement in turn can be used to
calculate the force experienced by the
mass so we would have all the necessary
elements to calculate the angular
velocity of the system while the
characteristics of these gyroscopes make
them ideal for a large number of
applications they have a disadvantage
although they are designed to measure
angular velocities linear accelerations
will also exert a force on the
oscillating mass and therefore if the
system is exposed to large accelerations
their accuracy would be compromised
but fortunately this is where the third
type of gyroscope we will discuss comes
in
optical gyroscopes which can detect
angular velocities completely
independently of the linear
accelerations of the system
these types of gyroscopes work on the
basis of the sagnac effect let's
consider a ring composed of fiber optics
and suppose that two beams of light
generated by a laser propagate in
opposite directions inside the ring if
the system is static both beams will
travel around the perimeter of the ring
in the same amount of time however if
the system is rotating this will no
longer be the case the beam emitted in
the same direction as the rotation of
the system will have to travel a longer
distance before reaching the end of the
path since the end point will basically
be moving away from it on the contrary
the beam traveling in the opposite
direction of the rotation of the system
will travel a shorter distance because
the end point will be getting closer to
it this difference in the distance
traveled by the light beams is the key
to calculating the angular velocity of
the system at this point you may be
wondering if a variation in travel time
was already generated with each beam
individually then why do we need two
beams to calculate the angular velocity
the reason is that since we are dealing
with the speed of light which remember
is approximately 300 000 kilometers per
second it would be extremely difficult
to make a system precise enough to
accurately measure the time from the
time that light is emitted until it
reaches the end point since this occurs
virtually instantaneously
since light is an electromagnetic wave
with a certain frequency and wavelength
by having two beams of light traveling
in opposite directions they interfere
with each other generating a resulting
beam with new characteristics
the characteristics of this new beam are
related to the phase difference between
the beams that produced it and therefore
to the difference in distances traveled
ultimately allowing us to calculate the
angular velocity
this type of gyroscope is not only
highly accurate but also quite reliable
because unlike the previous ones it is
able to operate completely without
moving parts
moreover despite the fact that in the
beginning they used to be of a large
size due to their technical requirements
nowadays this is no longer a limitation
since in 2018 scientists at caltech were
able to build an optical gyroscope of
just two millimeters square
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