Question

A long thin uniform rod of mass m and length L has a solid uniform sphere of mass M and radius R at one end. It pivots around a point that is L/2 from the left end of the rod. Find the moment of inertia of this object.

Answer 1

To find the moment of inertia of the given object, calculate the moment of inertia of the rod and the sphere separately and then use the parallel-axis theorem to find the moment of inertia of the combined object.

Step-by-step explanation:

The moment of inertia of an object depends on its shape and mass distribution. To calculate the moment of inertia of the given object, we need to determine the moment of inertia of the rod and the sphere separately and then use the parallel-axis theorem to find the moment of inertia of the combined object.

1. The moment of inertia of the rod is given by M(L^2)/12, where M is the mass of the rod and L is its length.
2. The moment of inertia of the solid sphere is given by (2/5)MR^2, where M is the mass of the sphere and R is its radius.
3. Using the parallel-axis theorem, the moment of inertia of the combined object about the given pivot point is M(L^2)/12 + (2/5)MR^2 + M(L/2)^2.