This gives the moment of inertia about the y axis for a coordinate systemĭouble ix = PolygonInertiaCalculator.ix(poly) ĭouble iy = PolygonInertiaCalculator.iy(poly) ĭouble ixy = PolygonInertiaCalculator.ixy(poly) ĪssertEquals(ix, (1.0 + 1.0/3.0), 1.0e-6) ĪssertEquals(iy, (21.0 + 1.0/3.0), 1. Import static ĭouble actual = PolygonInertiaCalculator.inertia(poly) ĪssertEquals(expected, actual, void testSquare()ĪssertEquals(expected, actual, void testRectangle() Here's the JUnit test to accompany it: import Scale = dot(poly, poly) + dot(poly, poly) + dot(poly, poly) Moment of A Force About a Point - Statics of Rigid Bodies Yu Jei Abat 88.3K subscribers Subscribe 33K views 2 years ago Statics of Rigid Bodies Hi guys, simple discussion all about the moment. We define the magnetic dipole moment to be a vector pointing out of the plane of the current loop and with a magnitude equal to the product of the current and loop area: The area vector, and thus the direction of the magnetic dipole moment, is given by a right-hand rule using the direction of the currents. If ((poly != null) & (poly.length > MIN_POINTS))įor (int n = 0 n < (poly.length-1) ++n) * poly of 2D points defining a closed polygon * Calculate moment of inertia about x-axis Public static double cross(Point2D u, Point2D v) Mtf is the component of the moment orthogonal to Ft in the plane Ï, while Mto is the component of Mt along Ft. The plane Ï is the plane containing the vectors Ft and Mt. Public static double dot(Point2D u, Point2D v) For 3D, the following image illustrates the geometry that we are solving on, where Ftnet force vector and Mtnet moment vector. Here's some code that might help you, along with a JUnit test to prove that it works: import 2D There's a parallel axis theorem that allows you to translate from one coordinate system to another.ĭo you know precisely which moment and coordinate system this formula applies to? Why do we break up vectors into components Two-dimensional motion is more complex than one-dimensional motion since the velocities can point in diagonal. When you have a 2D polygon, you have three moments of inertia you can calculate relative to a given coordinate system: moment about x, moment about y, and polar moment of inertia. You need to understand exactly what this formula means. I think you have more work to do that merely translating formulas into code.
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