Test: Gyroscope - Mechanical Engineering MCQ

Concept:

Axis of spin:

The rotor of engine of the vehicle is rotated about a particular axis, that axis of rotation referred to as the axis of spin.

In general, the axis of rotation of any engine considered as the axis of spin as a reference axis for the further calculation.

Axis of precession:

The motion of direction of initial angular momentum is known as precession and axis about which precession takes place is known as the axis of precession.

Applied gyroscopic couple:

The couple which appears due to change in the direction of angular momentum is known as an applied gyroscopic couple or gyroscopic torque.

And to achieve the effective gyroscopic effect, above three planes must be perpendicular to each other.

Concept:

The gyroscopic couple is given as, 

C = Iωω_p

where I = moment of inertia, ω = Angular velocity or spin velocity, ωp = Angular velocity of precession.

Calculation:

Given:

I = 30 kgm², N = 800 rpm, R = 170 m, V = 240 km/hr

Concept:

Gyroscopic Couple = I x ω x ω_p

Where I is the moment of inertia of the ship, ω_p is the angular velocity of precision and ω is the rotational speed of the ship

Calculation:

Given:

I = 200 kgm²,  ω = 200 rad/s

Gyroscopic Couple = 200 × 200 × 0.05 = 2000 Nm

Concept:

When a spinning disc undergoes precession then the torque applied is gyroscopic couple.

Gyroscopic couple = I × ω × ω_p

Where, ω = spinning angular velocity, ω_p = angular velocity of precession, I = mass moment of Inertia

Calculation:

Given:

T = 100 N.m, ω = 20 rad/s, I = 1 kg-m²

T = I × ω × ω_p

⇒ 100 = 1 × 20 × ω_p

ω_p = 5 rad/s

Gyroscopic moment is given by,

M = Iωω_p

 

Here it is a case of rolling.

In the case of rolling of a ship the axis of precession (ie longitudinal axis) is always parallel to the axis of spin of the stabilising rotor for all position. 

Hence there is no gyroscopic moment acting on the body of a ship.

Given that, the Air Screw of an Aeroplane rotates clockwise. when viewed from the rear end and the Aeroplane takes right turn, Then

 

From the Above Figure:

OA = Angular momentum vector before turning

OB = Angular momentum vector after turning

AB = Active gyroscopic couple

A'B' = reactive gyroscopic couple whose value is equal to the active gyroscopic couple but opposite in direction.

In the figure, vector AB is perpendicular to the plane of the applied couple which is in an anticlockwise direction when viewed from the left side of the plane. With the help of the Right-Hand Screw Rule, we observe that the Reactive couple will be in Clockwise Direction which tends to raise the tail and depress the nose.

Heavy steering:

• Heavy steering refers to when the steering wheel of your vehicle becomes stiff, making it difficult to turn.

Causes:

• Tyre pressure: If your tyres are not pumped up to the recommended air pressure, this can cause heavy steering. This is especially common in underinflated tyres, as it can mean the grip between the tyre and the road surface is compromised due to incorrect tyre pressure, and steering becomes more difficult.
• Wheel alignment: If your wheels are not aligned properly, this can also affect steering. If the front-end alignment is out of place, this can lead to uneven tyre wear on the front tyres – making the vehicle pull to the side, which can create heavy steering.
• Lack of fluid oil: Lack of fluid oil in your vehicle, or fluid leakage, can lead to heavy steering. If there is a lack of fluid oil or a leak, this can reduce the pressure in the system, meaning the steering wheel does not receive enough supply of fluid to perform freely.
• Thick fluid oil: On the other hand, thick fluid oil can lead to problems, too. Powering steering fluid can collect debris and dirt over time, which can mean it becomes too thick to flow freely and lubricate all parts of the system. This is a common cause of heavy steering at low speeds.

Concept:

Gyroscopic Couple = I × ω × ω_p

Where I is the moment of inertia of the flywheel, ωp is the angular velocity of spin and ω is the rotational speed of the flywheel

Calculation:

Given, W = 981/π kgf ⇒ m =  981/π kg, radius of gyration k = 100 cm = 1m, ω = 6rad/s, N = 100 r.p.m,

1 kgf = 9.81 N

⇒ T = 2000 kgf-m

For the effect of the gyroscopic couple to occur, the axis of precession should always be perpendicular to the axis of spin.

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If, however, the axis of precession becomes parallel to the axis of spin, there will be no effect of the gyroscopic couple acting on the body of the ship.

In the case of rolling a ship, the axis of precession (i.e. longitudinal axis) is always parallel to the axis of spin for all positions. Hence, there is no effect of the gyroscopic couple acting on the body of a ship.

Gyroscopic moment is given by,

M = Iωω_p

 

Here it is a case of rolling.

In the case of rolling of a ship the axis of precession (ie longitudinal axis) is always parallel to the axis of spin of the stabilising rotor for all position. 

Hence there is no gyroscopic moment acting on the body of a ship.