gyroscopic couple experiment

Gyroscopic Couple Basic | Principle | Examples

Table of Contents

Introduction to Gyroscopic 

Gyroscopic Couple Basic -‘Gyre’ is a Greek word, meaning ‘circular motion’ and Gyration means the whirling  motion. A gyroscope is a spatial mechanism which is generally employed for the study of precessional motion of a rotary body. Gyroscope finds applications in gyrocompass, used in aircraft, naval ship, control system of missiles and space shuttle.

GYROSCOPIC COUPLE

Direction of spin vector, precession vector and couple/torque vector .

• Turn the spin vector through 90 degree in the direction of  precession on the XOZ plane
• The turned spin vector will then correspond to the direction of active  gyroscopic couple/torque vector
• The reactive gyroscopic couple/torque vector is taken  opposite  to active gyro vector direction

Examples Of Gyroscopic Couples : 

Gyroscopic effect on ship , gyroscopic effect on aeroplane , stability of automotive.

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• Balancing of Inertia Forces
• Belt and Rope Drives Brakes
• Dynamics of Geared Systems
• Engine Governors
• Gear Trains
• General Dynamical Problems
• Inertia Forces and Couples
• Screw Threads
• The Geometry of Gears
• Turning Moment Diagrams
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Introduction

Angular displacement, velocity and acceleration, gyroscopic couple.

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Angular Displacement

• The direction of the axis of rotation in space.
• The sense of the angular displacement, i.e., whether clockwise or anti-clockwise.
• The magnitude of the angular displacement.
• The arrow head points along the vector in the same direction as a right handed screw would move relative to a fixed nut.

Angular Velocity

• If the direction of the angular displacement vector is constant, i.e., the plane of the angular displacement does not change its direction, then the angular velocity is merely the change in magnitude of the angular displacement with respect to time.

Angular Acceleration

23287/Gyroscopes-0002.png cannot be found in /users/23287/Gyroscopes-0002.png. Please contact the submission author.

• The direction of this acceleration vector is at right angles to the angular velocity vector and lies in the plane of motion of the velocity vector.

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Example - Example 1

Gyroscopic Effects in Engineering

• First Online: 01 July 2022

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• Ryspek Usubamatov   ORCID: orcid.org/0000-0001-8928-9389 2  

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The Industrial Revolution forced scientists and practitioners to devise new analytical methods to design machines and devices for solutions to technical problems. New industrial time is manifested by an intensification of the work of machinery in which rotating objects have shown the action of intricate inertial forces and motions that are called gyroscopic effects. Later, this property will be used in many devices for aviation, space, and other industries. Contemporary research of the dynamics of rotating objects solved many gyroscope problems in engineering based on the principles and rules of classical mechanics. This chapter contains two sections. The first is a brief history of gyroscopic effects and applications in the aerospace and ship industries.

The short classifications of the gyroscopes, their characteristics, technical data, and area of applications. The second section presents information about the fundamental laws, physical units and dimensions, and principles of engineering mechanics. This information is used for mathematical modeling of acting forces on rotating objects, and their motions that are used for describing the physics of gyroscopic effects. The knowledge of the basis of classical mechanics enables to solve the wide engineering problems of industries related to gyroscopic devices and their practical applications.

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Usubamatov, R. (2022). Gyroscopic Effects in Engineering. In: Theory of Gyroscopic Effects for Rotating Objects. Springer, Cham. https://doi.org/10.1007/978-3-030-99213-2_1

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What Is a Gyroscope?

A gyroscope is defined as

The device has a spinning disc mounted on the base so that it can move freely in more than one direction so that the orientation is maintained irrespective of the movement in the base.

Gyroscope Diagram

Parts of Gyroscope

A gyroscope consists of the following parts:

• Gyroscope frame

Design of Gyroscope

A gyroscope can be considered a massive rotor fixed on the supporting rings known as the gimbals. The central rotor is isolated from the external torques with the help of frictionless bearings that are present in the gimbals. The spin axis is defined by the axle of the spinning wheel.

The rotor has exceptional stability at high speeds as it maintains the high-speed rotation axis at the central rotor. The rotor has three degrees of rotational freedom.

Gyroscope Working Principle

The working principle of a gyroscope is based on gravity. It is explained as the product of angular momentum, which is experienced by the torque on a disc to produce a gyroscopic precession in the spinning wheel.

This process is termed gyroscopic motion or gyroscopic force and is defined as a rotating object’s tendency to maintain its orientation.

We know that the rotating object possesses angular momentum, which needs to be conserved. This is done because when there is any change in the axis of rotation, there will be a change in the orientation, which changes the angular momentum. Therefore, it can be told the working principle of the gyroscope is based on the conservation of angular momentum.

Read More: Angular Momentum

Types of Gyroscopes

The following are the three types of gyroscopes:

• Mechanical gyroscope
• Optical gyroscope
• Gas-bearing gyroscope

Mechanical Gyroscope

The working principle of the mechanical gyroscope is based on the conservation of angular momentum. This is also one of the most commonly known gyroscopes. The mechanical gyroscope is dependent on the ball bearing to spin. These gyroscopes are replaced with modern forms of gyroscopes as they are noisier. They find applications in the navigation of large aircraft and missile guidance.

Optical Gyroscopes

These gyroscopes are dependent on the ball bearing or the rotating wheel. They are also not based on the conservation of angular momentum . Optical gyroscopes use two optic fibre coils spun in different orientations. Since there is no movement in the optical gyroscopes, these are considered to be durable and find applications in modern spacecraft and rockets.

Gas-Bearing Gyroscopes

In a gas-bearing gyroscope, the friction between the moving parts is reduced by suspending the rotor with the help of pressurized gas. NASA used a gas-bearing gyroscope in the development of the Hubble telescope. Compared to the other gyroscopes, gas-bearing is quieter and more accurate.

Watch the video and learn more about gyroscopic effect experiment

Applications of Gyroscope

• Gyroscopes find applications in the compasses of boats, spacecraft, and aeroplanes. The aeroplane’s orientation and pitch are determined against the steady spin of the gyroscope.
• In spacecraft, the desired target’s navigation is done with a gyroscope’s help. The spinning centre of the gyroscope is used as the orientation point.
• The stabilization of the large boats and satellites is done with the help of massive gyroscopes.
• Gyroscopes are used in gyrotheodolites to maintain the direction in tunnel mining.
• Gyroscopes and accelerometers are used in the design of smartphones providing excellent motion sensing.

Read More: Acceleration

What Is the Difference between Accelerometer and Gyroscope?

An accelerometer is an instrument used to measure acceleration and detect vibrations. The other way of defining an accelerometer is an electromechanical device that measures forces due to acceleration.

Watch the video and learn how angular velocity works

Frequently Asked Questions – FAQs

What does a gyroscopic couple mean.

A gyroscopic couple is a turning moment in which the gyroscope’s axis of rotation is inclined so that the changes are opposite.

What is the expression for gyroscopic couple?

The expression for the gyroscopic couple is given as: C = I.⍵.⍵p Where,

• C is the gyroscopic couple
• I is the moment of inertia
• ⍵ is the angular velocity
• ⍵p is the angular velocity of precession

What is gyroscopic torque?

The gyroscopic torque is the torque applied to the rotating body such that there is a change in the axis of rotation of the rotating body.

State true or false: When viewed from the tail, an aeroplane’s engine spins in a clockwise manner. The plane turns to the right. As a result, the influence of the gyroscopic couple on the aeroplane can be stated to be from the dip to the tail.

The given statement is true.

What is the degree of freedom for gyroscope rotor?

The degree of freedom for the gyroscope rotor is 3.

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Lab Manual | To determine gyroscopic couple on Motorized Gyroscope.

AIM :- To determine gyroscopic couple on Motorized Gyroscope.

APPARATUS USED:- Four wheeler & two wheeler vehicle.

THEORY :- When a body moves along a curved path with a uniform linear velocity, a force in the direction of centripetal acceleration (known as centripetal force) has to be applied externally over the body, so that it moves along the required curved path. This external force applied is known as active force. When a body, itself, is moving with uniform linear velocity along a circular path, it is subjected to the centrifugal force radially outwards. This centrifugal force is called reactive force.

The change in angular momentum is known as active gyroscopic couple(I.ω.ω p ). When the axis of spin itself moves with angular velocity ω p , the disc is subjected to reactive couple whose magnitude is same (i.e. I.ω.ω p ) but opposite in direction to that of active couple.

OBSERVATION :-

• Mass of the vehicle (m) = ———— kg.
• Weight of the vehicle (W) = ——— Newtons.
• Radius of the wheels (r w ) = ———– metres.
• Radius of curvature ( R ) = ———– meters.
• Distance of centre of gravity, vertically above the road surface(h) = ———– metres,
• Width of track (x) = ——————–metres,
• Mass moment of inertia of one of the wheels( I w ) = —————–kg-m 2
• Angular velocity of the wheels or velocity of spin(ω w ) = ————rad/sec
• Mass moment of inertia of the rotating parts of the engine(I E ) = ———- kg-m 2
• Angular velocity of the rotating parts of the engine (ω E ) = ————rad/sec
• Gear ratio = ω E /ω w
• Linear velocity of the vehicle (ν) = r w ω w
• Angle of heal (θ) = ——– rad.

CALCULATION :-

For 4-wheel drive:

• Gyroscopic couple due to 4 wheels, C w = 4 I w ω w ω p where, (ω p = ν/R)
• Gyroscopic couple due to the rotating parts of the engine, , C E = I E ω E ω p = I w. G. ω w. ω p
• Net Gyroscopic couple, C = C w ± C E

For 2-wheel drive:

• Gyroscopic couple, C 1 = ν (2 I w ± I E . . G) cosθ /R. r w

PRECAUTIONS :-

• When rotating parts of the engine rotate in opposite directions, then negative sign is used.
• When C E ›C w , then C will be negative. Thus the reaction will be vertically downwards on the outer wheels and vertically upwards on the inner wheels.
• The gyroscopic couple will act over the vehicle outwards i.e. in the anticlockwise direction when seen from the front of the vehicle. The tendency of this couple is to overturn the vehicle in outward direction.
• Gyroscopic couple of four wheel drive is = ————–N-m.
• Gyroscopic couple of two wheel drive is = ————–N-m.

VIVA – QUESTIONS :-

• Write a short note on gyroscope.
• What do you understand by gyroscopic couple ? Derive a formula for its magnitude.
• Explain the application of gyroscopic principles to aircrafts.
• Discuss the effect of the gyroscopic couple on a two wheeled vehicle when taking a turn.
• When the pitching of a ship is upward, the effect of gyroscopic couple acting on it will be to move the ship towards port side or to move the ship towards star-board.

Related posts:

• Lab Manual | Gyroscopic Effect
• Lab Manual | static balancing on static balancing machine

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Alfred Franklin Varghese , Chenthil Jegan Thangaraj Mariapushpam , Joseph Sekhar Santhappan , Sreeja Viswaksenan , Amjith Lilly Ravindran , Bavanish Balac , Archana Beena Suresh , Murugan Paradesi Chockalingam , Godwin Glivin , Raichel Nivetha Xavier , Hareesh Krishnan Harikumar; Experimental determination of gyroscopic couple. AIP Conf. Proc. 26 January 2024; 3059 (1): 030008. https://doi.org/10.1063/5.0193759

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A spatial mechanism commonly employed for the control of angular motion of a body is called Gyroscope. The resistance to change in the direction of rotational axis is called the gyroscopic effect. The torque or turning moment, that opposes any change of the inclination of the axis of rotation of a gyroscope, is called gyroscopic couple. Or in other words, whenever the axis of a rotating body is caused to change direction, a couple is required, called as gyroscopic couple. The reaction to this couple is experienced in aircraft, marine and car engines when changing direction and is also employed in navigating systems. In the present study, a motorized gyroscope apparatus is used to evaluate the active and reactive gyroscopic couple. The apparatus is made up of a brass gyroscope flywheel mounted in a cradle which allows the flywheel to pivot in the x, y and z directions. When the gyroscopic couple is equal to the couple applied by the counterbalance weight; the arm of the gyroscope will run in a horizontally. When the arm of the gyroscope is horizontal, the speed of precession and the spin speed have to be recorded. Knowing the mass properties of the flywheel in addition to these speeds, the gyroscopic couple can be estimated experimentally. From the mass of counterbalance weight and the radius of rotation, the theoretical couple that can be produced by the apparatus can be evaluated. Reasonably good agreement was observed between test and theoretical results.

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Questions and answers, what is the equation used to calculate the gyroscopic couple and what do its variables represent.

The equation is T = I ω ωp, where T is the applied couple, I is the moment of inertia, ω is the angular velocity, and ωp is the precession rate.

Explain the principle of angular momentum as it applies to gyroscopes.

The principle of angular momentum states that a gyroscope maintains its orientation due to the conservation of angular momentum, resisting changes in its axis of rotation.

In what way do gyroscopes function differently when under the influence of external torque?

When external torque is applied, the orientation of the spin axis changes, but the amount and direction of this change differs from what would occur if the disk were not spinning.

List two applications of gyroscopes in modern technology.

<p>Gyroscopes are used in inertial navigation systems and to stabilize flying vehicles such as drones.</p> Signup and view all the answers

What role do gyroscopes play in minimizing the effects of waves on ships?

<p>Gyroscopes help reduce rolling and pitching effects caused by waves, enhancing the stability of ships.</p> Signup and view all the answers

Describe the orientation change of a disc spinning about its axis under precession.

<p>As the disc spins about its spin axis, it precesses about a perpendicular axis when an external torque is applied, creating a rotational movement.</p> Signup and view all the answers

What is the significance of the moment of inertia in the gyroscopic couple equation?

<p>The moment of inertia, I, is significant as it quantifies the rotational resistance of the gyroscope, influencing the gyroscopic couple's magnitude.</p> Signup and view all the answers

How does the angular velocity of a gyroscope relate to its precession?

<p>The angular velocity, ω, affects the rate of precession, ωp; higher angular velocity generally results in a greater precession rate when torque is applied.</p> Signup and view all the answers

What is the relationship between angular momentum and angular velocity for the disc mentioned in the content?

<p>The angular momentum of the disc is given by the equation $L = I \omega$, where $L$ is angular momentum, $I$ is the mass moment of inertia, and $\omega$ is the angular velocity of the disc.</p> Signup and view all the answers

How does the axis of spin OX change during precession according to the text?

<p>During precession, the axis of spin OX rotates anticlockwise about the axis OY through a small angle $\delta\theta$.</p> Signup and view all the answers

What is the significance of the couple $I \omega \omega_p$ in relation to the disc?

<p>The couple $I \omega \omega_p$ represents the active gyroscopic couple that must be applied to the disc to facilitate its precession.</p> Signup and view all the answers

Define the plane of precession and the axis of precession as described in the content.

<p>The plane of precession is defined as the horizontal plane XOZ, while the axis of precession is the perpendicular axis OY.</p> Signup and view all the answers

What happens to the angular momentum vector as the axis OX is turned through a small angle $\delta\theta$?

<p>As the axis OX is turned through a small angle $\delta\theta$, the angular momentum vector changes from $\mathbf{ox}$ to $\mathbf{ox'}$.</p> Signup and view all the answers

What does the rate of change of angular momentum signify when a couple is applied to the disc?

<p>The rate of change of angular momentum signifies the influence of the applied couple on the movement of the disc, given by $\frac{dL}{dt} = I \omega \frac{\delta\theta}{dt}$.</p> Signup and view all the answers

Explain the orientation of the vector $xx'$ in relation to the vertical plane XOY.

<p>In the case of a very small displacement $\delta\theta$, the vector $xx'$ is perpendicular to the vertical plane XOY.</p> Signup and view all the answers

What is the role of angular velocity $\omega_p$ in the context of gyroscopic precession?

<p>The angular velocity $\omega_p$ describes the speed of rotation of the axis of spin about the axis of precession OY.</p> Signup and view all the answers

What is the significance of the plane XOY in the context of angular momentum?

<p>The plane XOY is where the active gyroscopic couple acts, and it is crucial for understanding the behavior of angular momentum.</p> Signup and view all the answers

Describe the reactive gyroscopic couple and how it is generated.

<p>The reactive gyroscopic couple is generated when the axis of spin rotates about the axis of precession, and it acts in the opposite direction to the active couple.</p> Signup and view all the answers

What dimensions and properties are specified for the disc in the mechanical engineering lab?

<p>The disc has a radius of $0.135$ m, a mass of $5.2$ kg, and a distance of weight from the center of rotation of $0.17$ m.</p> Signup and view all the answers

What procedure should be followed to conduct the experiment with the disc?

<p>The experiment involves switching on the motor to a steady speed, setting the pointer to zero, adding known weights, and recording the angular displacement time.</p> Signup and view all the answers

What precautions must be taken before starting the gyroscopic experiment?

<p>Precautions include checking all fastenings, ensuring the rotor is balanced, periodically lubricating bearings, and placing the base on a leveled platform.</p> Signup and view all the answers

Why is it important to limit rotor speed to 1500 rpm during the experiment?

<p>Limiting the rotor speed to 1500 rpm prevents potential damage to the equipment and ensures safe operating conditions.</p> Signup and view all the answers

What role do bearings play in the generation of the gyroscopic couple?

<p>Bearings support the shaft and resist the gyroscopic couple by exerting an equal and opposite couple.</p> Signup and view all the answers

How does the position of the weight affect the angular displacement during the experiment?

<p>The position of the weight affects the torque applied on the disc, thus influencing the time taken for angular displacement.</p> Signup and view all the answers

How would you calculate the actual torque (Tact) given the weight and distance from the center of rotation?

<p>Tact is calculated using the formula Tact = W × L, where W is the weight in Newtons and L is the distance in meters.</p> Signup and view all the answers

What is the formula for calculating the theoretical torque (Ttheoretical) in terms of moment of inertia and angular velocities?

<p>Theoretical torque is calculated as Ttheoretical = I × ω × ωp, where I is the moment of inertia, ω is the angular velocity, and ωp is the angular velocity of precision.</p> Signup and view all the answers

Explain how to find the angular velocity (ω) in rad/sec from the speed of the disc (N) in rpm.

<p>Angular velocity can be calculated using the formula ω = 2 π N / 60, converting revolutions per minute into radians per second.</p> Signup and view all the answers

What does 'k' represent in the context of the moment of inertia (I) calculation?

<p>'k' represents the radius of gyration, which is a measure of how mass is distributed relative to the axis of rotation.</p> Signup and view all the answers

How is the angular velocity of precision (ωp) calculated using the angle turned (θ) and time taken (t)?

<p>The angular velocity of precision is calculated using the formula ωp = (θ/t) × (π/180), converting degrees to radians over time.</p> Signup and view all the answers

If you know the weight on the arm and the distance from the center, how can Tact be affected by increasing the distance?

<p>Increasing the distance L will increase the actual torque (Tact), as torque is directly proportional to both the weight and the distance from the pivot.</p> Signup and view all the answers

What impact does increasing the moment of inertia (I) have on the theoretical torque (Ttheoretical)?

<p>Increasing the moment of inertia (I) will directly increase the theoretical torque (Ttheoretical), assuming angular velocities remain constant.</p> Signup and view all the answers

Define the significance of Tact in assessing the performance of a rotational system.

<p>Tact represents the actual torque generated by a system, indicating its effectiveness and efficiency in performing work.</p> Signup and view all the answers

Study Notes

Aim of the experiment.

• Justification of the gyroscopic couple equation ( T = I \omega \omega_p ).
• Involves observation and measurement of independent variations in applied couple ( T ) and precession ( \omega_p ).

Apparatus Used

• Stopwatch for timing measurements.
• Dead weights for applying force to the gyroscope.

Theory Overview

• A gyroscope measures or maintains orientation, relying on angular momentum preservation.
• Comprises a spinning wheel or disc with a freely orienting axle.
• Changes in orientation respond to external torque but differ in magnitude and direction compared to a non-spinning disc.

Applications of Gyroscopes

• Used in inertial navigation systems (e.g., Hubble telescope).
• Important for stabilizing flying vehicles like drones and helicopters.
• Operate in ship systems to reduce rolling and pitching from waves.
• Used in aeroplanes and monorail systems.

Key Concepts in Gyroscopic Motion

• Spinning disc with angular velocity ( \omega ) (anticlockwise viewed from the front).
• Plane of spinning is parallel to the vertical plane, with axis of precession perpendicular to both axes OX and OZ.

Angular Momentum and Precession

• Angular momentum defined as ( I \omega ), with ( I ) being the moment of inertia.
• Axis of spin processes about the axis OY at an angular velocity ( \omega_p ).
• Active gyroscopic couple generated as ( I \omega \omega_p ) in the horizontal plane (XOZ).
• Reactive couple equal in magnitude but opposite in direction opposes the active couple.

Specifications of Equipment

• Radius of disc: ( r = 13.5 \times 10^{-2} ) m.
• Mass of disc: ( m = 5.2 ) kg.
• Distance of weight from the center: ( L = 17 \times 10^{-2} ) m.

Procedure Steps

• Start the motor attached to the disc and stabilize speed.
• Set the precision axis pointer to zero degrees.
• Add known weights to the loading arm and time the angular displacement.
• Repeat with increasing weights while resetting the pointer each time.

Precautions to Follow

• Ensure all fastenings are secure before starting.
• Check rotor balance prior to operation.
• Regularly lubricate bearings to ensure smooth function.
• Operate on a leveled platform to prevent measurement errors.
• Do not exceed rotor speeds of 1500 RPM to avoid accidents.

Observation and Calculation

• Measure and record load, speed, angles, and times for angular displacement.
• Calculate actual torque ( T_{act} = W \times L ) where ( W ) is the weight.
• Calculate theoretical torque ( T_{theoretical} = I \times \omega \times \omega_p ).
• Compare actual torque with theoretical calculations to validate the gyroscopic equation.

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Description.

This quiz focuses on the experimental validation of the gyroscopic couple equation T= I ω ωp. Participants will explore the principles of gyroscopic motion through observation and measurement. Understanding the relationship between applied couples and precession rates is key to mastering this topic in mechanical engineering.

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LABORATORY REPORT MOTORIZED GYROSCOPE

AIM To find the gyroscope couple on a motorized gyroscope experimentally and compare with applied couple. APPARATUS Motorized gyroscope THEORY Precession a common lecture demonstration of gyroscopic precession is to hang a bicycle wheel by one end of its axle. If the bicycle wheel is not spinning, it flops down. But if the wheel is spinning, it doesn't fall. Instead it precesses around: its axle rotates in a horizontal plane. The torque of the weight adds some spin about the y-axis, perpendicular to the original spin. The resulting spin axis is turned a little in the xy-plane. The torque doesn't change the value of the spin; instead it " curves " the spin. This phenomemon can easily be studied by means of a gyroscope. If we attempt to move some of its parts, it does not only resist this motion but even evades it. This resistance to change in the direction of rotational axis is called the gyroscopic effect. The gyroscopic couple is given as : C = I x ωp x ωs

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