Nine experiments are reported on the ability of people to perceive the distances reachable with hand-held rods that they could wield by movements about the wrist but not see. An observed linear relation between perceived and actual reaching distances with the rods held at one end was found to be unaffected by the density of the rods, the direction relative to the body in which they were wielded, and the frequency at which they were wielded. Manipulating (a) the position of an attached weight on an otherwise uniformly dense rod and (b) where a rod was grasped revealed that perceived reaching distance was governed by the principal moment(s) of inertia (I) of the hand-rod system about the axis of rotation. This dependency on moment of inertia (I) was found to hold even when the reaching distance was limited to the length of rod extending beyond an intermediate grasp. An account is given of the haptic subsystem (hand-muscles-joints-nerves) as a smart perceptual instrument in the Runeson (1977) sense, characterizable by an operator equation in which one operator functionally diagonalizes the inertia and strain tensors. Attunement to the invariants of the inertia tensor over major physical transformations may be the defining property of the haptic subsystem. This property is discussed from the Gibsonian (ecological) perspectives of information as invariants over transformations and of intentions as extraordinary constraints on natural law.