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The moment of inertia of a cube depends on what its axis of rotation is. About an axis perpendicular to one of its sides and through the centre of the cube is (ML2)/6. Where M is the Mass of the Cube and L the length of its side. Due to the symmetry of the cube, you can find the Moment of Inertia about almost any other axis by using Parallel and Perpendicular Axis Theorems.
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∙ 14y ago
Wiki User
∙ 11y agoThis would depend on what axis the rod is rotating about. For a rod with length L and an evenly distributed mass m:
About an axis that is perpendicular to the rod and located at the end of the rod:
I_end = (m*L^2)/3
About an axis that is perpendicular to the rod and located at the center of the rod:
I_center = (m*L^2)/12
For this next axis we need radius (r) of rod instead of length...
About an axis along(parallel) the rod and though it's center of mass:
I_along = (m*r^2)/2
For any other kinds of axis the parallel axis theorem should be used in the following manner:
M: total mass of body (rod).
d: The perpendicular distance from the actual axis of rotation to an axis which is both parallel with the axis of rotation and at the same time passes through the body's center of mass (com).
I_com: The moment of inertia around this parallel axis that passes though the body's center of mass.
I_d: The moment of inertia around rotational axis.
The parallel axis theorem then states that:
I_d = I_com+M*d^2
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What happens to moment of inertia of thin rod when its length is doubled?
Since its length is doubled, the number of molecules present increase, resulting in an increase in mass of the rod. And we all know that mass is directly proportional to inertia, therefore the moment of inertia also increases.
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