Gyroscope Questions

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Very Short Answers Questions [1 Mark Questions]

Ques. The rotor of the gyroscope has _______ degrees of rotational freedom.

1. Three
2. Four
3. One
4. Two

Ans. The correct answer is a. Three

Explanation: The rotor is forced to spin around an axis that is always perpendicular to the axis of the inner gimbal during operation. As a result, the rotor has three degrees of rotational freedom, whereas the gyroscope axis has two.

Ques. The signal-to-noise ratio of the gyroscope is lower.

1. True
2. False

Ans. The correct answer is b. False

Explanation: A gyroscope has a higher signal-to-noise ratio.

Ques. Gyroscopes work on the principle of

1. Conservation of energy
2. Conservation of linear momentum
3. Conservation of angular momentum
4. None of the above

Ans. The correct answer is c. Conservation of angular momentum

Explanation: The operation of a gyroscope depended on gravity. It is defined as the product of angular momentum, which is experienced by the torque on a disc and causes gyroscopic precession in the spinning wheel.

Ques. The gyroscope is used to measure all types of rotation but fails in identifying movement.

1. True
2. False

Ans. The correct answer is a. True

Explanation: To measure all types of rotation, a gyroscope is used while an accelerometer is used for measuring linear movement.

Ques. What is the conservation of angular momentum?

Ans. The conservation of angular momentum is defined as the tendency of a system to maintain its rotational momentum in the absence of external torque

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Short Answers Questions [2 Marks Questions]

Ques. What is torque? Is it a scalar or a vector quantity?

Ans. The torque of an object describes its rotational force. It causes a body to rotate about an axis. Mathematical, it is given by the product of the force applied on the body and perpendicular distance from the axis of rotation.

Torque is a vector quantity and it is denoted by the symbol tau (τ).

Ques. What is an accelerometer?

Ans. An accelerometer is a device that measures acceleration and detects vibrations. An accelerometer is a type of electromechanical device that detects acceleration forces.

Ques. What are gimbals?

Ans. A gimbal is a pivoted support that allows an item to be rotated about an axis. A system of three gimbals, one positioned on top of the other with orthogonal pivot axes, can be utilized to allow an object mounted on the innermost gimbal to stay independent of its support's rotation.

Ques. Why are gyroscopes used in navigation?

Ans. Gyroscopes give fixed reference directions or turning rate data, whereas accelerometers assess changes in system velocity. The computer analyses data on changes in direction and acceleration and sends it to the vehicle's navigation system.

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Long Answers Questions [3 Marks Questions]

Ques. Give an application of the gyroscope.

Ans. Applications of gyroscopes are

• Gyroscope is used in the compasses of spacecraft, boats, and airplanes. 
• It is also used to stabilize satellites and large boats. 
• Gyroscopes are also used in gyro theodolites to maintain tunnel mining orientation. 
• To provide motion sensing, smartphones use gyroscopes and accelerometers.

Ques. What are the properties of gyroscopes?

Ans. The followings are the properties of gyroscopes

• In the absence of external torques, the angular momentum of a gyroscope remains constant.
• Gyroscopes exhibit precession i.e. a phenomenon when a torque is applied perpendicular to the axis of rotation of a gyroscope, its axis of rotation changes direction.
• They are helpful for navigation systems and stabilizing devices because of their excellent stability and resilience to changes in direction.
• Because of their gyroscopic inertia, gyroscopes resist changes in the rotational state.

Ques. What are the applications of fiber optic gyroscopes?

Ans. The followings are the application of fiber optic gyroscopes

• They are used in High-shock applications such as gun-pointing systems. However, due to their sensitivity to vibrations, they are frequently combined with multiple-axis FOG and accelerometers.
• They are used in high-performance space applications
• Fiber optic gyrocompasses are used in navigation systems
• They are used in Inertial navigation systems of guided missiles
• They are used in Remotely-operated vehicles and autonomous underwater vehicles.

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Very Long Answers Questions [5 Marks Questions]

Ques. A cylindrical disc of a gyroscope of mass m = 15 kg and radius r = 5.0 cm spins with an angular velocity ω = 330 rad/s. The distance between the bearings in which the axle of the disc is mounted is equal to l = 15 cm. The axle is forced to oscillate about a horizontal axis with a period T = 1.0 s and amplitude ɸ_m = 20°. Find the maximum value of the gyroscopic forces exerted by the axle on the bearings in Newton.

Ans. Given

• Mass of the cylindrical disc of the gyroscope, m = 15 kg
• The radius of the cylindrical disc of a gyroscope, r = 5 cm
• Angular velocity, ω = 330 rad/s
• Distance between the bearing, l = 15 cm

The moment of inertia is given by

I = 1/2 mr²

Angular momentum is given by

L = mr².ω

The axis oscillates about a horizontal axis making an instantaneous angle

ϕ = ϕ_m sin 2πt/T

The axle is forced to oscillate about a horizontal axis with a period T = 1.0 s and amplitude ɸ_m = 20°.

The maximum value of the rate of precession, dϕ/dt = 2πɸ_m/T

When precession is maximum, torque on the axle is given by

τ = Iω dϕ/dt

⇒ τ = 1/2 mr² x ω x 2πɸ_m/T

⇒ τ = (πmr² ω ɸ_m) / T

Gyroscopic force can be given by

F = τ/l = (πmr² ω ɸ_m) / Tl

On substituting the values, we get

F = [3.14 x 15 x (5 x 10^-2)² x 330 x 20] / [1 x 15 x 10^-2]

⇒ F = 90 N

Ques. State and explain the types of a gyroscope.

Ans. There are three major types of a gyroscope

• Mechanical Gyroscopes: The operating principle of mechanical gyroscopes is based on the conservation of angular momentum. These gyroscopes rely on a ball bearing to spin, but they have been replaced by current gyroscopes since they are louder.
• Optical Gyroscopes: These gyroscopes do not based on angular momentum conservation. They are dependent on a ball bearing or a rotating wheel. These gyroscopes make use of two optic fiber coils spun in opposing directions. Optical gyroscopes are considered strong since they do not move.
• Gas-Bearing Gyroscopes: The friction between the moving elements of a gas-bearing gyroscope is decreased by suspending the rotor with compressed gas. Gas-bearing gyroscopes are quieter and more accurate than other varieties.

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