The rotational inertia of a thin cylindrical shell of mass M, radius R, and length L about its central axis (X - X') is: A) MR²/2 B) ML²/2 C) ML² D) MR² E) none of these

Question

Quizplus · Accepted Answer

The rotational inertia of a thin cylindrical shell is given by 1/2MR^2, and since this cylindrical shell has a length L, the parallel axis theorem can be used to find the total rotational inertia about the central axis by adding the rotational inertia about the axis passing through the center of mass and perpendicular to the length (which is 1/2MR^2) to the product of the mass and the square of the distance from the center of mass to the central axis (which is 1/4ML^2 for a cylinder). Therefore, the total rotational inertia is: 1/2MR^2 + 1/4ML^2 = M(R^2 + L^2/4) = MR², which matches answer choice D.

The Rotational Inertia of a Thin Cylindrical Shell of Mass