Inertia Of Object Research Articles

A Biomechanical Evaluation of Resistance

Newton's second law of motion describes the acceleration of an object as being directly proportional to the magnitude of the net force, in the same direction as the net force and inversely proportional to its mass (a = F/m). With respect to linear motion, mass is also a numerical representation of an object's inertia, or its resistance to change in its state of motion and directly proportional to the magnitude of an object's momentum at any given velocity. To change an object's momentum, thereby increasing or decreasing its velocity, a proportional impulse must be generated. All motion is governed by these relationships, independent of the exercise being performed or the movement type being used; however, the degree to which this governance affects the associated kinematics, kinetics and muscle activity is dependent on the resistance type. Researchers have suggested that to facilitate the greatest improvements to athletic performance, the resistance-training programme employed by an athlete must be adapted to meet the specific demands of their sport. Therefore, it is conceivable that one mechanical stimulus, or resistance type, may not be appropriate for all applications. Although an excellent means of increasing maximal strength and the rate of force development, free-weight or mass-based training may not be the most conducive means to elicit velocity-specific adaptations. Attempts have been made to combat the inherent flaws of free weights, via accommodating and variable resistance-training devices; however, such approaches are not without problems that are specific to their mechanics. More recently, pneumatic-resistance devices (variable) have been introduced as a mechanical stimulus whereby the body mass of the athlete represents the only inertia that must be overcome to initiate movement, thus potentially affording the opportunity to develop velocity-specific power. However, there is no empirical evidence to support such a contention. Future research should place further emphasis on understanding the mechanical advantages/disadvantages inherent to the resistance types being used during training, so as to elicit the greatest improvements in athletic performance.

Perceptual behavior: recurrence analysis of a haptic exploratory procedure.

Various object properties are perceptible by wielding. We asked whether the dynamics of wielding differed as a function of the to-be-perceived property. Wielding motions were analyzed to determine if they differed under the intention to perceive or not perceive rod length (experiment 1), to perceive object height versus object width (experiment 2), and to perceive the length forward of where the rod was grasped versus the position of the grasp (experiment 3). Perceiving these different properties is known to depend on different components of the object's inertia tensor. Analyses of the subtle recurrent patterns in the phase space of the hand motions revealed differences in wielding across the different perceptual intentions. Haptic exploratory procedures may exhibit distinct exploratory dynamics.

Affordance, proper function, and the physical basis of perceived heaviness

The physical basis of perceived heaviness requires consideration of the haptic perceptual system's role in controlling actions (the system's proper function) and the relation of an object's inertial properties to properties of the human movement system (the object's affordance). We show that the mass of a wielded object and particular scalar variables calculated from the object's inertia tensor combine linearly in determining perceived heaviness. The tensor-derived scalars reflect the symmetry and volume of the corresponding inertia ellipsoid. These measures bear directly on the object's wieldability, that is, on the patterning and level of muscular forces required to move the object in a controlled fashion.

Perception of Object Length by Sound

Although hearing is classically considered a temporal sense, everyday listening suggests that subtle spatial properties constitute an important part of what people know about the world through sound. Typically neglected in psychoacoustics research, the ability to perceive the precise sizes of objects on the basis of sound was investigated during the routine event of dropping wooden dowels of different lengths onto a hard surface. In two experiments, the ordinal and metrical success of naive listeners was related to length but not to the simple acoustic variables (duration, amplitude, frequency) likely to be related to it. Additional analysis suggests the potential relevance of an object's inertia tensor in constraining perception of that object's length, analogous to the case that has been made for perceiving length by effortful touch.

Inertia as reaction of the vacuum to accelerated motion

It was proposed by Haisch, Rueda and Puthoff (Phys. Rev. A, 49, 678, 1994) that the inertia of matter could be interpreted at least in part as a reaction force originating in interactions between the electromagnetic zero-point field (ZPF) and the elementary charged consitutents (quarks and electrons) of matter. Within the limited context of that analysis, it appeared that Newton's equation of motion, f=ma, could be inferred from Maxwell's equations as applied to the ZPF, i.e. the stochastic electrodynamics (SED) version of the quantum vacuum. We report on a new approach which avoids the ad hoc particle-field interaction model (Planck oscillator) of that analysis, as well as its concomitant formulational complexity. Instead, it is shown that a non-zero ZPF momentum flux arises naturally in accelerating coordinate frames from the standard relativistic transformations of electromagnetic fields. Scattering of this ZPF momentum flux by an object will yield a reaction force that may be interpreted as a contribution to the object's inertia. This new formulation is properly covariant yielding the relativistic equation of motion. Our approach is related by the principle of equivalence to Sakharov's conjecture of a connection between Einstein action and the vacuum. If correct, this concept would substitute for Mach's principle and imply that no further mass-giving Higgs-type fields may be required to explain the inertia of material objects, although extensions to include the zero-point fields of the other fundamental interactions may be necessary for a complete theory of inertia.

Eigenvalues of the inertia tensor and exteroception by the “muscular sense”

Muscle spindles and Golgi tendon organs constitute the receptor foundation to the “muscle sense”. Muscle sensitivity has long been assumed relevant to the non-visual perception of the positions and motions of the body's segments and of the properties of hand-held objects. Dynamic touch is the label given to the particular kind of tactile exteroperception that involves a non-spatial input from muscles and tendons. When a hand-held object is wielded, hefted, carried and so on, the hand movements, together with the physical properties of the object, produce torques and angular motions that change in time with the movement. There is, however, an unchanging quantity that relates the variable torques and angular motions, namely, the object's inertia for rotation about a fixed point in the wrist. Our research revealed that the non-visual perception of the length of a wielded object by dynamic touch is a function of muscular sensitivity to the principal moments or eigenvalues of the inertia tensor. Across four experiments, variations in object length were accompanied by variations in width, spatial and material heterogeneity, the relation of the tensorial components to mass, and geometric shape. Subjects had no foreknowledge of the variations in object dimensions. Perceived lengths of occluded objects were reported by adjusting a visible marker so that its position corresponded to the position of the felt end of the object. In each experiment, perceived length was closely related to actual length and uniquely constrained by the major and minor eigenvalues of the inertia tensor. The present results, in conjunction with previous research, suggest that the inertia tensor provides the domains for two sets of functions realized by the “muscular sense” one consisting of the principal moments of inertia or eigenvalues, which map on to perceived object magnitudes (e.g. length, weight), and one consisting of the principal directions or eigenvectors, which map on to perceived relations between hand and object (e.g. position of grasp). The significance of information-perception specificity over cognitive mechanisms is underlined and perspectives on dynamic touch and its underlying muscular sensitivity, including a general tensorial analysis, are discussed.

Perceiving by Dynamic Touch the Distances Reachable With Irregular Objects

Observers wielded occluded objects and reported the distances reachable with the distal tips of the objects. Each object consisted of a cylindrical stem with two branches attached perpendicularly along its length; stem and branch lengths varied across objects. In Experiment 1, the branches were 180 deg. apart, both attached halfway along the stem. In Experiment 2, the branches were 180 deg. apart, one at one fourth and the other at three fourths of the stem length. In Experiment 3, the branches were 90 deg. apart, one at one fourth and the other at three fourths of the stem length. Observers had no foreknowledge of the objects' shapes. In each experiment, perceived reachable distance was found to be dependent on the maximum eigenvalue of the object's inertia tensor computed about the point of rotation in the wrist. Discussion focused on (a) quantifying shape for dynamic touch through the inertia ellipsoid, (b) the significance of the inertia tensor to the spatial abilities of dynamic touch, and (c) contra...

Eigenvectors of the inertia tensor and perceiving the orientation of a hand-held object by dynamic touch.

Subjects wielded an object, hidden from view, and reported the orientation in which the object was positioned in the hand. The object consisted of a stem with two branches forming a V attached perpendicularly to the stem's distal end. The branches were differentially weighted so that the same spatial orientation of the object was associated with different orientations of its principal (symmetry) axes or eigenvectors. Perceived orientation was found to be dependent on the eigenvectors of the object's inertia tensor, computed about the point of rotation in the wrist, rather than on its spatial orientation. The results underscore the significance of the inertia tensor to understanding the perception of spatial properties by dynamic touch.