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An engine, connected with a flywheel, is designed to operate at an average angular speed of 800 rpm. During operation of the engine, the maximum change in kinetic energy in a cycle is found to be 6240 J. In order to keep the fluctuation of the angular speed within ±1% of its average value, the moment of inertia (in kg-m2) of the flywheel should be ____________.
(Important - Enter only the numerical value in the answer)
Correct answer is '44.45'. Can you explain this answer?
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A certain limit, a flywheel with a moment of inertia of 0.1 kg·m² is used.
To calculate the maximum fluctuation of the angular speed, we can use the formula for the change in kinetic energy of a rotating object:
ΔK = (1/2) I ω²
Where ΔK is the change in kinetic energy, I is the moment of inertia, and ω is the angular speed.
We can rearrange this formula to solve for ω:
ω² = (2ΔK) / I
Plugging in the given values:
ω² = (2 * 6240 J) / 0.1 kg·m²
ω² = 124800 J / kg·m²
Now we can take the square root of both sides to find ω:
ω = √(124800 J / kg·m²)
ω ≈ 353.55 rad/s
Since the engine is designed to operate at an average angular speed of 800 rpm, we can convert this to rad/s:
800 rpm * (2π rad/rev) * (1 min/60 s) ≈ 83.78 rad/s
The fluctuation of the angular speed is the difference between the maximum and average angular speeds:
Fluctuation = ω - average angular speed
Fluctuation = 353.55 rad/s - 83.78 rad/s
Fluctuation ≈ 269.77 rad/s
Therefore, in order to keep the fluctuation of the angular speed within a certain limit, the flywheel is designed to reduce the fluctuation to approximately 269.77 rad/s.
To calculate the maximum fluctuation of the angular speed, we can use the formula for the change in kinetic energy of a rotating object:
ΔK = (1/2) I ω²
Where ΔK is the change in kinetic energy, I is the moment of inertia, and ω is the angular speed.
We can rearrange this formula to solve for ω:
ω² = (2ΔK) / I
Plugging in the given values:
ω² = (2 * 6240 J) / 0.1 kg·m²
ω² = 124800 J / kg·m²
Now we can take the square root of both sides to find ω:
ω = √(124800 J / kg·m²)
ω ≈ 353.55 rad/s
Since the engine is designed to operate at an average angular speed of 800 rpm, we can convert this to rad/s:
800 rpm * (2π rad/rev) * (1 min/60 s) ≈ 83.78 rad/s
The fluctuation of the angular speed is the difference between the maximum and average angular speeds:
Fluctuation = ω - average angular speed
Fluctuation = 353.55 rad/s - 83.78 rad/s
Fluctuation ≈ 269.77 rad/s
Therefore, in order to keep the fluctuation of the angular speed within a certain limit, the flywheel is designed to reduce the fluctuation to approximately 269.77 rad/s.
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An engine, connected with a flywheel, is designed to operate at an average angular speed of 800rpm. During operation of the engine, the maximum change in kinetic energy in a cycle is foundto be 6240 J. In order to keep the fluctuation of the angular speed within ±1% of its averagevalue, the moment of inertia (in kg-m2) of the flywheel should be ____________.(Important - Enter only the numerical value in the answer)Correct answer is '44.45'. Can you explain this answer?
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An engine, connected with a flywheel, is designed to operate at an average angular speed of 800rpm. During operation of the engine, the maximum change in kinetic energy in a cycle is foundto be 6240 J. In order to keep the fluctuation of the angular speed within ±1% of its averagevalue, the moment of inertia (in kg-m2) of the flywheel should be ____________.(Important - Enter only the numerical value in the answer)Correct answer is '44.45'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about An engine, connected with a flywheel, is designed to operate at an average angular speed of 800rpm. During operation of the engine, the maximum change in kinetic energy in a cycle is foundto be 6240 J. In order to keep the fluctuation of the angular speed within ±1% of its averagevalue, the moment of inertia (in kg-m2) of the flywheel should be ____________.(Important - Enter only the numerical value in the answer)Correct answer is '44.45'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An engine, connected with a flywheel, is designed to operate at an average angular speed of 800rpm. During operation of the engine, the maximum change in kinetic energy in a cycle is foundto be 6240 J. In order to keep the fluctuation of the angular speed within ±1% of its averagevalue, the moment of inertia (in kg-m2) of the flywheel should be ____________.(Important - Enter only the numerical value in the answer)Correct answer is '44.45'. Can you explain this answer?.
An engine, connected with a flywheel, is designed to operate at an average angular speed of 800rpm. During operation of the engine, the maximum change in kinetic energy in a cycle is foundto be 6240 J. In order to keep the fluctuation of the angular speed within ±1% of its averagevalue, the moment of inertia (in kg-m2) of the flywheel should be ____________.(Important - Enter only the numerical value in the answer)Correct answer is '44.45'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about An engine, connected with a flywheel, is designed to operate at an average angular speed of 800rpm. During operation of the engine, the maximum change in kinetic energy in a cycle is foundto be 6240 J. In order to keep the fluctuation of the angular speed within ±1% of its averagevalue, the moment of inertia (in kg-m2) of the flywheel should be ____________.(Important - Enter only the numerical value in the answer)Correct answer is '44.45'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An engine, connected with a flywheel, is designed to operate at an average angular speed of 800rpm. During operation of the engine, the maximum change in kinetic energy in a cycle is foundto be 6240 J. In order to keep the fluctuation of the angular speed within ±1% of its averagevalue, the moment of inertia (in kg-m2) of the flywheel should be ____________.(Important - Enter only the numerical value in the answer)Correct answer is '44.45'. Can you explain this answer?.
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