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As radius of gyration is indirectly to the parallel axis theorem, parallel axis theorem uses the ____________ of the distance.
- a)Square root
- b)Square
- c)Cube root
- d)Cube
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
As radius of gyration is indirectly to the parallel axis theorem, para...
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. And uses the square of the distance from the axis of rotation.
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As radius of gyration is indirectly to the parallel axis theorem, para...
Parallel Axis Theorem and Distance
The parallel axis theorem relates the moment of inertia of an object around an axis to the moment of inertia of the object around a parallel axis. This theorem is based on the distance between the two axes.
Square of the Distance
The parallel axis theorem states that the moment of inertia of an object around a parallel axis is equal to the moment of inertia of the object around its center of mass plus the mass of the object times the square of the distance between the two axes.
Formula
Mathematically, the parallel axis theorem can be expressed as I_parallel = I_cm + md^2, where:
- I_parallel is the moment of inertia around the parallel axis,
- I_cm is the moment of inertia around the center of mass,
- m is the mass of the object, and
- d is the distance between the two axes.
Importance of Square of Distance
The square of the distance in the parallel axis theorem emphasizes the relationship between the moment of inertia of an object and the distance between the axis of rotation. This square term highlights the fact that the moment of inertia increases quadratically with the distance from the axis of rotation.
Conclusion
Therefore, as the parallel axis theorem uses the square of the distance, it is essential to consider this relationship when calculating the moment of inertia of an object around a parallel axis. Understanding the significance of the square term in the theorem helps in accurately determining the moment of inertia and analyzing the rotational motion of objects.
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As radius of gyration is indirectly to the parallel axis theorem, parallel axis theorem uses the ____________ of the distance.a)Square rootb)Squarec)Cube rootd)CubeCorrect answer is option 'B'. Can you explain this answer?
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