How to calculate the moment of inertia of a right triangular slab: another method! скачать в хорошем качестве

How to calculate the moment of inertia of a right triangular slab: another method!

In the previous video, we showed how to calculate the moment of inertia of a right triangular slab by slicing into thin rods perpendicular to the rotation axis. This time, we calculate the moment of inertia of a triangle by slicing into thin rods parallel to the rotation axis! 🧠 Access full flipped physics courses with video lectures and examples at https://www.zakslabphysics.com/ The moment of inertia contribution of a thin rod parallel to the rotation axis is the same as the moment of inertia of a point mass, and this is because all the mass is located at the same distance from the axis of rotation. We find an expression for the moment of inertia contribution of the slice dI in terms of both x and y, then we have to use the equation of the line connecting vertices of the triangle to relate y to x. Once dI is expressed in terms of a single variable, we are ready to integrate dI (the integral is a summation device for adding up infinitely many infinitesimal contributions). We find the moment of inertia for the triangular slab, but we still have to sub in an expression for the area density in terms of mass and total area. Once that's done, we arrive at the same answer for the moment of inertia of a right triangle about one edge: 1/6*M*b^2.