Moment of Inertia
Definition
An object's resistance to changes in its rotation — the rotational equivalent of mass.
Symbol: · Unit: kg·m²
Technical definition
Defined as I = Σmᵢrᵢ² (discrete) or ∫r²dm (continuous), measuring mass distribution relative to the rotation axis. Appears in rotational dynamics: τ = Iα and rotational KE = ½Iω².
Example
A hoop and a solid disk of equal mass and radius: the hoop (mass farther out) has I = MR², twice the disk's ½MR² — so the disk wins a roll-down-a-ramp race.
Common confusion
Moment of inertia depends on the axis, not just the object. The same rod has a different I spinning about its center versus its end. Always specify the axis — I is meaningless without it.