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What is parallel axis theorem and to whom it is applied?
- a)Theorem used to add the two mutually perpendicular moment of inertias for areas
- b)Theorem used to add the two mutually perpendicular moment of inertias for volumes
- c)Theorem used to add the two mutually perpendicular moment of inertias for linear distances
- d)Theorem used to add the two mutually perpendicular moment of inertias for vectors
Correct answer is option 'A'. Can you explain this answer?
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What is parallel axis theorem and to whom it is applied?a)Theorem used...
Parallel axis for any area is used to add the two mutually perpendicular moment of inertias for areas. It gives a moment of inertia perpendicular to the surface of the body. That is the moment of inertia perpendicular to the surface in considerance.
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What is parallel axis theorem and to whom it is applied?a)Theorem used...
The Parallel Axis Theorem
The parallel axis theorem is a fundamental principle in physics and engineering that allows us to calculate the moment of inertia of an object about an axis parallel to a given axis. It is used to determine the moment of inertia of an object that is not rotating about its center of mass.
Application of the Theorem
The parallel axis theorem is applied to calculate the moment of inertia for areas, not volumes, as stated in option A. This theorem is used in mechanics and engineering to analyze the rotational motion of objects.
Explanation of the Theorem
The theorem states that the moment of inertia of an object about an axis parallel to its center of mass is equal to the sum of its moment of inertia about its center of mass and the product of its mass and the square of the distance between the two axes.
Mathematical Formulation
Mathematically, the parallel axis theorem can be expressed as:
I = Icm + md²
Where:
- I is the moment of inertia about the parallel axis
- Icm is the moment of inertia about the center of mass axis
- m is the mass of the object
- d is the distance between the two axes
Example
Let's consider a rectangular plate with a mass of 2 kg, length of 4 m, and width of 2 m. The moment of inertia about an axis passing through its center of mass and parallel to its length can be calculated as follows:
Icm = (1/12) * m * (l² + w²)
= (1/12) * 2 * (4² + 2²)
= 2/12 * 20
= 10/6
Now, let's say we want to calculate the moment of inertia about an axis parallel to the length but located at one end of the plate. The distance between the two axes is half the length of the plate, which is 2 m.
Using the parallel axis theorem, we can calculate the moment of inertia about this axis:
I = Icm + md²
= 10/6 + 2 * 2²
= 10/6 + 8
= 58/6
Therefore, the moment of inertia about the parallel axis is 58/6 kg·m².
Conclusion
In summary, the parallel axis theorem is a fundamental principle used to calculate the moment of inertia of an object about an axis parallel to its center of mass. It is widely applied in mechanics and engineering to analyze the rotational motion of objects.
The parallel axis theorem is a fundamental principle in physics and engineering that allows us to calculate the moment of inertia of an object about an axis parallel to a given axis. It is used to determine the moment of inertia of an object that is not rotating about its center of mass.
Application of the Theorem
The parallel axis theorem is applied to calculate the moment of inertia for areas, not volumes, as stated in option A. This theorem is used in mechanics and engineering to analyze the rotational motion of objects.
Explanation of the Theorem
The theorem states that the moment of inertia of an object about an axis parallel to its center of mass is equal to the sum of its moment of inertia about its center of mass and the product of its mass and the square of the distance between the two axes.
Mathematical Formulation
Mathematically, the parallel axis theorem can be expressed as:
I = Icm + md²
Where:
- I is the moment of inertia about the parallel axis
- Icm is the moment of inertia about the center of mass axis
- m is the mass of the object
- d is the distance between the two axes
Example
Let's consider a rectangular plate with a mass of 2 kg, length of 4 m, and width of 2 m. The moment of inertia about an axis passing through its center of mass and parallel to its length can be calculated as follows:
Icm = (1/12) * m * (l² + w²)
= (1/12) * 2 * (4² + 2²)
= 2/12 * 20
= 10/6
Now, let's say we want to calculate the moment of inertia about an axis parallel to the length but located at one end of the plate. The distance between the two axes is half the length of the plate, which is 2 m.
Using the parallel axis theorem, we can calculate the moment of inertia about this axis:
I = Icm + md²
= 10/6 + 2 * 2²
= 10/6 + 8
= 58/6
Therefore, the moment of inertia about the parallel axis is 58/6 kg·m².
Conclusion
In summary, the parallel axis theorem is a fundamental principle used to calculate the moment of inertia of an object about an axis parallel to its center of mass. It is widely applied in mechanics and engineering to analyze the rotational motion of objects.
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What is parallel axis theorem and to whom it is applied?a)Theorem used to add the two mutually perpendicular moment of inertias for areasb)Theorem used to add the two mutually perpendicular moment of inertias for volumesc)Theorem used to add the two mutually perpendicular moment of inertias for linear distancesd)Theorem used to add the two mutually perpendicular moment of inertias for vectorsCorrect answer is option 'A'. Can you explain this answer?
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What is parallel axis theorem and to whom it is applied?a)Theorem used to add the two mutually perpendicular moment of inertias for areasb)Theorem used to add the two mutually perpendicular moment of inertias for volumesc)Theorem used to add the two mutually perpendicular moment of inertias for linear distancesd)Theorem used to add the two mutually perpendicular moment of inertias for vectorsCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about What is parallel axis theorem and to whom it is applied?a)Theorem used to add the two mutually perpendicular moment of inertias for areasb)Theorem used to add the two mutually perpendicular moment of inertias for volumesc)Theorem used to add the two mutually perpendicular moment of inertias for linear distancesd)Theorem used to add the two mutually perpendicular moment of inertias for vectorsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is parallel axis theorem and to whom it is applied?a)Theorem used to add the two mutually perpendicular moment of inertias for areasb)Theorem used to add the two mutually perpendicular moment of inertias for volumesc)Theorem used to add the two mutually perpendicular moment of inertias for linear distancesd)Theorem used to add the two mutually perpendicular moment of inertias for vectorsCorrect answer is option 'A'. Can you explain this answer?.
What is parallel axis theorem and to whom it is applied?a)Theorem used to add the two mutually perpendicular moment of inertias for areasb)Theorem used to add the two mutually perpendicular moment of inertias for volumesc)Theorem used to add the two mutually perpendicular moment of inertias for linear distancesd)Theorem used to add the two mutually perpendicular moment of inertias for vectorsCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about What is parallel axis theorem and to whom it is applied?a)Theorem used to add the two mutually perpendicular moment of inertias for areasb)Theorem used to add the two mutually perpendicular moment of inertias for volumesc)Theorem used to add the two mutually perpendicular moment of inertias for linear distancesd)Theorem used to add the two mutually perpendicular moment of inertias for vectorsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is parallel axis theorem and to whom it is applied?a)Theorem used to add the two mutually perpendicular moment of inertias for areasb)Theorem used to add the two mutually perpendicular moment of inertias for volumesc)Theorem used to add the two mutually perpendicular moment of inertias for linear distancesd)Theorem used to add the two mutually perpendicular moment of inertias for vectorsCorrect answer is option 'A'. Can you explain this answer?.
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