Parallel Axis Theorem — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Parallel Axis Theorem Gives the moment of inertia about any axis parallel to one through the centre of mass, separated by perpendicular distance d. Valid for any rigid body. Take an axis through the centre of mass (CM) and a parallel axis a distance d away. Write the moment of inertia about the parallel axis as a sum over mass elements: I = m i r i 2. Express each r i in terms of its distance from the CM axis and the offset d; expand the square. The cross term vanishes because m i x i = 0 about the CM (definition of centre of mass). What remains is I = I cm + Md 2. d 0 The two axes must be parallel I cm is taken about an axis through the centre of mass Using the distance between two arbitrary axes instead of the distance from the centre-of-mass axis — the theorem only works when one axis passes through the CM. Forgetting to square d, or adding Md instead of Md 2. Applying it to add two non-parallel axes; the axes must be parallel.