Nparallel axis theorem pdf files

Generalization of parallel axis theorem for rotational inertia. Compute the product of inertia with respect to the xyaxes by dividing the section into three rectangles. Computing the intersection of two oriented bounding rectangles now that we have a better understanding of the separating axis theorem, we will introduce. What links here related changes upload file special pages permanent link page information wikidata item cite this page. Media in category steiners parallel axis theorem the following 11 files are in this category, out of 11 total. The parallel axis theorem, also known as huygenssteiner theorem, or just as steiners. Moment of inertia of a triangle with respect to a centroidal axis, 3 36 1 2 3 1 2 3 1 12 2 1 2. Moment of inertia itof a circular area with respect to a tangent to the circle, 4 4 5 4 2 2 4 2 1. Rigid body, moment of inertia, centre of gravity, axis of rota tion, torsional vibration, spring constant, angular restoring force.

Moment of inertia illinois institute of technology. It must be specified with respect to a chosen axis of rotation. The perpendicular axis theorem states that the moment of inertia of a planar lamina about an. And so i about the end axis is 112 ml squared plus the mass times l over 2 square and a 12 plus a quarter is ml squared. Because the x axis is an axis of symmetry for the strip, di xy 0 and eq. Parallel axis theorem and perpendicular axis theorem are used for calculating the moment of inertia of a body considering the mass of the body and moment of inertia from the center of gravity.

Moment of inertia through scaling and the parallel axis theorem. We place the origin of our coordinate system at the center ofmass cm. As an example, we use data from table 1 and the parallel axis theorem to identify that contribution of plate a to the moment of inertia i2 of the. Parallel axis theorem is used for asymmetrical bodies while perpendicular axis theorem is used for symmetrical bodies. Separating axis theorem for oriented bounding boxes.

The first term is the moment of inertia ir, the second term is zero by definition of the center of mass. Modify, remix, and reuse just remember to cite ocw as the source. Download32 is source for parallel axis theorem shareware, freeware download rsp parallel port connection ocx, parallel lap, webuzo for. Proof of the parallel axis theorem consider a rigid system of. For example, in the parallel axis theorem, the reference axis should be passing through the center of mass of the object. Suppose we want to calculate the moment of inertia of a uniform ring about its diameter. And that means that all you need to know is the moment through the center of mass, and you can calculate the moment through any other. The parallel axis theorem, also known as huygens steiner theorem, or just as steiners theorem, named after christiaan huygens and jakob steiner, can be used to determine the moment of inertia or the second moment of area of a rigid body about any axis, given the bodys moment of inertia about a parallel axis through the objects center of gravity and the perpendicular distance between the axes. What links here related changes upload file special pages permanent link page.