How a Gyroscope Works ⚡ What a Gyroscope Is

Summary

This 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

00:00

🌌 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.

05:02

🔄 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.

10:03

📳 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.

Keywords

💡Gyroscope

A gyroscope is a device that can measure and maintain orientation, providing information about angular velocity or orientation changes. In the video, it's described as having two main functions: indicating orientation relative to a reference axis and measuring the rate of orientation change. The gyroscope is central to the video's theme, as it is the main subject being explained and its applications are discussed in various contexts such as phones, aeronautics, and robotics.

💡Angular Velocity

Angular velocity is the rate at which an object rotates or revolves over time, measured in degrees per second. It is a key concept in the video, as gyroscopes measure this to determine how fast a system is rotating. The script explains how mechanical gyroscopes use precession to calculate angular velocity, and it's also used in the context of optical gyroscopes to determine system rotation.

💡Torque

Torque is the rotational equivalent of linear force and is defined as the cross product of the radius and the force applied. In the video, torque is essential for understanding how mechanical gyroscopes work, as it is the force that can cause a rotating system to change its orientation. The script mentions torque in the context of generating angular momentum and its role in the operation of mechanical gyroscopes.

💡Angular Momentum

Angular momentum is a measure of the quantity of rotation of an object and is determined by the object's moment of inertia and its angular velocity. The video script discusses angular momentum as a key factor in the operation of mechanical gyroscopes, explaining that it is conserved when no external torque acts on a rotating system.

💡Moment of Inertia

The moment of inertia is a measure of an object's resistance to changes in its rotation. It depends on the object's shape and mass distribution. In the video, the moment of inertia is important for calculating the angular momentum of a system and is a factor in the operation of mechanical gyroscopes, as it affects the system's response to applied torque.

💡Precession

Precession is a phenomenon where a rotating body undergoing an external force changes its orientation. In the video, precession is used to demonstrate how mechanical gyroscopes can determine the angular velocity of a system. The script provides an example of a bicycle wheel hanging by its axle to illustrate the concept of precession.

💡Coriolis Effect

The Coriolis effect is the apparent deflection of the path of an object moving in a rotating system. The video script explains how Coriolis effect vibrating gyroscopes operate, using the change in tangential velocity of a mass oscillating within a rotating system to calculate angular velocity. This effect is crucial for the functioning of certain types of modern gyroscopes found in electronic devices.

💡Sagnac Effect

The Sagnac effect is the difference in the time it takes for two light beams traveling in opposite directions in a rotating ring to complete their journey. The video describes how optical gyroscopes use the Sagnac effect to measure angular velocity by detecting the phase difference between the two light beams, which is related to the distance they travel due to the system's rotation.

💡Optical Gyroscope

An optical gyroscope is a device that uses the properties of light, such as the Sagnac effect, to measure angular velocity without moving parts. The video highlights the advantages of optical gyroscopes, including their high accuracy and reliability, and mentions a recent development where a tiny optical gyroscope was created, showcasing the technology's progress.

💡Vestibular System

The vestibular system is the sensory system of the inner ear that detects changes in head position and spatial orientation. The video script mentions the human body's built-in 'gyroscope' as the vestibular system, which provides us with a sense of balance and spatial orientation, drawing a parallel between biological and technological gyroscopes.

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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