Final answer:
The moment of inertia of a solid, uniform sphere of mass and radius about an axis that is tangent to its surface can be derived using the parallel axis theorem. The moment of inertia about a parallel axis is equal to the sum of the moment of inertia about the center of mass and the product of the mass and the square of the distance between the parallel axis and the center of mass. For a solid, uniform sphere, the moment of inertia about its center of mass is (2/5)MR², where M is the mass of the sphere and R is its radius. Using the parallel axis theorem, the moment of inertia about the parallel axis is (7/5)MR².
Step-by-step explanation:
The moment of inertia of a solid, uniform sphere of mass and radius about an axis that is tangent to its surface can be derived using the parallel axis theorem. The parallel axis theorem states that the moment of inertia about a parallel axis is equal to the sum of the moment of inertia about the center of mass and the product of the mass and the square of the distance between the parallel axis and the center of mass.
For a solid, uniform sphere, the moment of inertia about its center of mass is (2/5)MR², where M is the mass of the sphere and R is its radius. Let d be the distance from the center of mass to the parallel axis tangent to the surface.
Using the parallel axis theorem, the moment of inertia about the parallel axis is given by:
Iparallel-axis = Icenter of mass + md² = (2/5)MR² + Mr² = (7/5)MR²