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The moment of inertia of a thin rod of length l about the perpendicular axis through its centre is I the moment of inertia of the square structure made by 4 such rod about a perpendicular axis to the plane and through the centre will be what?
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The moment of inertia of a thin rod of length l about the perpendicula...
Understanding Moment of Inertia
The moment of inertia (I) is a measure of an object's resistance to changes in its rotation about an axis. For a thin rod of length l, the moment of inertia about an axis perpendicular to its length and passing through its center is given by:
- I (rod) = (1/12) * m * l^2, where m is the mass of the rod.
Square Structure Formation
To find the moment of inertia of a square structure formed by four such rods, we need to consider the arrangement:
- Rods Arrangement: Four rods are arranged in a square shape.
- Length of Each Rod: Each rod has length l.
- Mass of Each Rod: Assume the mass of each rod is m.
Moment of Inertia Calculation
The overall moment of inertia of the square structure about a perpendicular axis through its center can be derived as follows:
1. Rod Contribution: Each rod contributes to the total moment of inertia.
2. Positioning: Two rods are aligned along the x-axis and two along the y-axis, both passing through the center.
Using the parallel axis theorem and summing contributions:
- I (square) = 4 * I (rod) = 4 * (1/12) * m * l^2
- Simplification: I (square) = (1/3) * m * l^2.
Final Result
Thus, the moment of inertia of the square structure made by four thin rods about a perpendicular axis through the center is:
- I (square) = (1/3) * m * l^2.
This result shows how the configuration of the rods influences the overall moment of inertia, demonstrating the importance of shape and axis orientation in rotational dynamics.
The moment of inertia (I) is a measure of an object's resistance to changes in its rotation about an axis. For a thin rod of length l, the moment of inertia about an axis perpendicular to its length and passing through its center is given by:
- I (rod) = (1/12) * m * l^2, where m is the mass of the rod.
Square Structure Formation
To find the moment of inertia of a square structure formed by four such rods, we need to consider the arrangement:
- Rods Arrangement: Four rods are arranged in a square shape.
- Length of Each Rod: Each rod has length l.
- Mass of Each Rod: Assume the mass of each rod is m.
Moment of Inertia Calculation
The overall moment of inertia of the square structure about a perpendicular axis through its center can be derived as follows:
1. Rod Contribution: Each rod contributes to the total moment of inertia.
2. Positioning: Two rods are aligned along the x-axis and two along the y-axis, both passing through the center.
Using the parallel axis theorem and summing contributions:
- I (square) = 4 * I (rod) = 4 * (1/12) * m * l^2
- Simplification: I (square) = (1/3) * m * l^2.
Final Result
Thus, the moment of inertia of the square structure made by four thin rods about a perpendicular axis through the center is:
- I (square) = (1/3) * m * l^2.
This result shows how the configuration of the rods influences the overall moment of inertia, demonstrating the importance of shape and axis orientation in rotational dynamics.
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The moment of inertia of a thin rod of length l about the perpendicular axis through its centre is I the moment of inertia of the square structure made by 4 such rod about a perpendicular axis to the plane and through the centre will be what?
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The moment of inertia of a thin rod of length l about the perpendicular axis through its centre is I the moment of inertia of the square structure made by 4 such rod about a perpendicular axis to the plane and through the centre will be what? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The moment of inertia of a thin rod of length l about the perpendicular axis through its centre is I the moment of inertia of the square structure made by 4 such rod about a perpendicular axis to the plane and through the centre will be what? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The moment of inertia of a thin rod of length l about the perpendicular axis through its centre is I the moment of inertia of the square structure made by 4 such rod about a perpendicular axis to the plane and through the centre will be what?.
The moment of inertia of a thin rod of length l about the perpendicular axis through its centre is I the moment of inertia of the square structure made by 4 such rod about a perpendicular axis to the plane and through the centre will be what? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The moment of inertia of a thin rod of length l about the perpendicular axis through its centre is I the moment of inertia of the square structure made by 4 such rod about a perpendicular axis to the plane and through the centre will be what? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The moment of inertia of a thin rod of length l about the perpendicular axis through its centre is I the moment of inertia of the square structure made by 4 such rod about a perpendicular axis to the plane and through the centre will be what?.
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