Question

What is the moment of inertia I of this assembly about the axis through which it is pivoted?

Express the moment of inertia in terms of mr(mass of rod), m1,m2, and x. Keep in mind the length of the rod is 2x, not x.

Answer 1

Solution Formula for the moment of inertia Here, m, - Mass of the particle r. -Distance of the particle Moment of inertia due to the sphere of mass(m): Distance of (m) to the pivot point is x. Therefore, Moment of inertia due to the sphere of mass(m2) Distance of (m) to the pivot point is x. Therefore, Moment of inertia of the rod Distance of m, to the pivot point is Therefore, Moment of inertia I of this assembly about the axis through which it is pivoted is, Add equation (2), (3) and (4) Thus, the moment of inertia is I -xm m,