Question

The theorem relates the moment of inertia about any axis to the moment of inertia about a parallel axis through the centroid?

• A. Perpendicular axis theorem
• B. Parallel axis theorem
• C. Axis of symmetry theorem
• D. Centroidal axis theorem

Hint:

Moment of Inertia Theorems. Parallel Axis Theorem: \(I = I_c + Md^2\) (relates MOI about parallel axes). Perpendicular Axis Theorem: \(I_z = I_x + I_y\) (for plane lamina).

Answer 1

The Correct Option is B

The Parallel Axis Theorem provides a relationship between the moment of inertia of a rigid body about an axis passing through its center of mass (centroidal axis) and the moment of inertia about any other axis parallel to it.
The theorem states: $$ I = I_c + Md^2 $$ where \(I\) is the moment of inertia about the parallel axis, \(I_c\) is the moment of inertia about the parallel axis passing through the center of mass (centroid), \(M\) is the total mass of the body, and \(d\) is the perpendicular distance between the two parallel axes.
This theorem directly relates the moment of inertia about any parallel axis to the centroidal moment of inertia.
The Perpendicular Axis Theorem relates moments of inertia about axes within a plane lamina to the moment of inertia about an axis perpendicular to the lamina.