The discussion revolves around the moment of inertia of a two-dimensional rectangle with sides a and b, specifically questioning whether it depends on both dimensions when the axis of rotation is parallel to one of the sides and passes through the center of mass.
The discussion is ongoing, with participants examining different perspectives on the moment of inertia. Some guidance has been offered regarding the interpretation of the formula and the role of mass distribution, but no consensus has been reached.
Participants are considering the implications of the axis of rotation and how it affects the moment of inertia, with some expressing confusion about the dependence on both dimensions. There is an emphasis on understanding the physical setup and assumptions involved in the problem.
No. If the axis is, say, the y axis, think of the lamina as a set of parallel thin strips in the x direction. They'll all have the same moment. I think the formula you quoted would be right for an axis perpendicular to the lamina.peripatein said:Homework Statement
Will the moment of inertia of a two dimensional rectangle (with sides a, b) whose axis is parallel to one of its sides and passes through its center of mass, be (1/12)M(a2+b2)?
That's why I said to think of it as parallel strips across the axis. Adding more only increases the moment in proportion to the mass.peripatein said:It's not that something's wrong with that, simply that it seemed a bit strange it would not depend on the other side too.