1a. List the parameters that affect the moment of inertia. b. Which is the most
ID: 3160855 • Letter: 1
Question
1a. List the parameters that affect the moment of inertia. b. Which is the most important parameter and explain why? c. Explain the use of Parallel Axis Theorem and Perpendicular Axis Theorem. 1a. List the parameters that affect the moment of inertia. b. Which is the most important parameter and explain why? c. Explain the use of Parallel Axis Theorem and Perpendicular Axis Theorem. b. Which is the most important parameter and explain why? c. Explain the use of Parallel Axis Theorem and Perpendicular Axis Theorem. c. Explain the use of Parallel Axis Theorem and Perpendicular Axis Theorem.Explanation / Answer
Answer:
(a) Moment of inertia (I) is depends on both the distribution of mass in the body and the location of the axis of rotation.
Therefore, I = mr2.
(b) Both the mass distribution in the body and the location of the axis rotation are the most important parameters to define the moment of inertia of a particular body. It is not possible to write moment of inertia with a single parameter either mass m or location of axis of rotation. We need both parameters.
(c) Parallel axis theorem and perpendicular axis theorem are used to solve problems on moment of inertia.
Parallel axis theorem states that, the moment of inertia of I of a body about any axes is same as the moment of inertia IG about an axis parallel to the body passing through its center of gravity plus Mb2, where M is the mass of that body and b is the distance between the axis and the center of gravity.
That means, I = IG + Mb2
Perpendicular axis theorem, states that for any plane body, example a rectangular sheet the moment of inertia about any of its axes which are perpendicular to the plane is equal to the sum of the moment of inertia about any two perpendicular axes in the plane of the body which intersect the first axis in the plane, this theorem is used when the body is symmetric in shape about two out of the three axes, if moment of inertia about two of the axes are known the moment of inertia about the third axis can be found using the expression,
Ia = Ib + Ic
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