Rotational Motion
Class 11 · Rotational Motion
Radius of Gyration
k = √(I/M) — see equivalent ring radius for ring, disc, rod, sphere, shell.
Key Notes
01
k = √(I/M) is the distance from the axis at which all the mass, if concentrated as a thin ring, would give the same I.
02
Ring: k = R. Disc: k = R/√2. Solid sphere: k = R√(2/5). Hollow shell: k = R√(2/3). Rod about center: k = L/√12.
03
Useful in rolling motion: a = g sinθ / (1 + k²/R²).
Formulas
Definition
Equivalent ring radius.
Rolling acceleration
Smaller k/R → faster rolling.
Important Points
Hollow objects have larger k than solid ones of the same mass and radius.
k depends on the chosen axis — use parallel-axis theorem if shifted.
Radius of Gyration notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.