Intro to Moment of Inertia Practice Problems

A non-uniform thin spoke has a total length L. Its mass per unit length depends on the position x measured from the left end and is described by the function dm/dx = Ax where A has units kg/m². i) Determine its moment of inertia about a perpendicular axis through its left end (x = 0) using I = ∫r²dm. ii) Does its moment of inertia differ from the moment of inertia of a uniform spoke?

A child's entertainment equipment has a 100.0 cm long, thin and uniform rod of mass 0.500 kg. Determine the moment of inertia of the rod pivoted about its center such that it spins perpendicular to its length. 

You are given a thin spoke of mass 3.0 kg that is 100.0 cm long to be used in an experiment. Determine its moment of inertia if it rotates about a perpendicular axis through i) one of its ends ii) its center iii) a parallel axis through the spoke.