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Gas Giants: Jupiter and Saturn
Published in Thomas Hockey, Jennifer Lynn Bartlett, Daniel C. Boice, Solar System, 2021
Thomas Hockey, Jennifer Lynn Bartlett, Daniel C. Boice
Planetary scientists infer the radii of the different layers of Jupiter (and other planets) by measuring their moments of inertia. As we discussed earlier, the same push on a skateboard produces greater acceleration than on a car because a car has more mass. Another way of thinking about mass is to consider it the resistance of an object to changing its motion along a line, or linear inertia. For a rotating object, its resistance to change in its rotational motion is its moment of inertia. If you remove a wheel from that skateboard, you can spin it easily around the mounting axis. However, flipping it about the disk, or perpendicular to the mounting axis, is awkward. Moment of inertia depends upon how mass is distributed through a rotating body. Have you ever balanced and twirled a pencil on your finger? A dinner knife? A spoon? The uneven shape of a spoon makes it more challenging; its moment of inertia is greater.
Newton’s laws of motion
Published in Paul Grimshaw, Michael Cole, Adrian Burden, Neil Fowler, Instant Notes in Sport and Exercise Biomechanics, 2019
The moment of inertia of an object refers to the object’s ability to resist rotation. The larger the moment of inertia, the more the object will resist rotation. Similarly, the smaller the moment of inertia of an object, the less will be its resistance to start, stop or change its rotational state (Figure C7.1). The moment of inertia is calculated from the distribution of mass (m) about an axis of rotation (r). It can be expressed mathematically as I = m × r2. The moment of inertia of a body is related to a specific axis of rotation and there will be different moment of inertia values for each axis that the body is rotating about. For example, there may be a moment of inertia of the whole body about a longitudinal axis or about an anterior–posterior axis. Also, moment of inertia can be expressed for individual parts or individual segments of a body (e.g. the upper leg can have a moment of inertia about the hip joint axis of rotation or the lower leg a moment of inertia about the knee joint axis of rotation).
“Center of Mass Perception”: Affordances as Dispositions Determined by Dynamics
Published in John Flach, Peter Hancock, Jeff Caird, Kim Vicente, Global Perspectives on the Ecology of Human-Machine Systems, 2018
Geoffrey P. Bingham, Michael M. Muchisky
The size of an object of a given shape determines, for any given error distance, the repercussions of missing the CM. Ignoring torques around the opposition axis created by frictional forces, a miss of a given distance will produce less rotational acceleration of a larger object than of a smaller object. The greater the rotational acceleration, then for a given amount of rotation, the smaller the time in which to respond, or alternatively, within a given response time, the greater the amount of undesired rotation. However, shape, in addition to size, affects rotational acceleration. Both shape and size determine an object’s moment of inertia or resistance to rotation. Might shape and size interact in determining the accuracy of judgments of the center of mass? We should expect random errors in locating the CM to increase both as objects increase in size and as shapes become more elongated and less compact.
Effects of upper and lower body wearable resistance on spatio-temporal and kinetic parameters during running
Published in Sports Biomechanics, 2020
Grace A. Couture, Kim D. Simperingham, John B. Cronin, Anna V. Lorimer, Andrew E. Kilding, Paul Macadam
All loading conditions, excluding WB10%, failed to elicit significant differences in spatio-temporal variables compared to ULPre. Despite LB loading at a wider range of loads, the present study showed no increase in SL. This opposes the findings of Martin (1985) who divided and applied a 1.0-kg load (1.4% BM) to each foot, while in the current study load (LB1% 0.6–0.9 kg; LB3% 1.8–2.7 kg; LB5% 3.0–4.5 kg) was evenly distributed around the thighs and shank, not centralised to the feet. When Martin (1985) applied the same load to the thigh, no spatio-temporal differences were observed. Inertia refers to the tendency of an object to resist changes in their current state, static or moving. Adding mass to an object will increase its inertia, requiring more energy to start or stop motion. Half a kilogram added to the thigh increased inertia for the leg about the hip approximately 2%, while adding the same load to the feet increased inertia by 13% (Martin, 1985). In contrast, LB loading in the present study was designed to retain limb balance and minimise inertial effects. Therefore, the varying inertial effect created by load placement could explain the differences between the results of this study and those of Martin (1985), despite the higher loading used.
Head and neck size and neck strength predict linear and rotational acceleration during purposeful soccer heading
Published in Sports Biomechanics, 2018
Jaclyn B. Caccese, Thomas A. Buckley, Ryan T. Tierney, Kristy B. Arbogast, William C. Rose, Joseph J. Glutting, Thomas W. Kaminski
Our findings suggest that greater head and neck size predicted lower peak linear and rotational accelerations (Figure 2(A) and (B); Figure 3(A) and (B)). According to Newton’s Second Law (Force = mass × linear acceleration), higher head mass should result in lower linear head accelerations. Similarly, torque = moment of inertia × rotational acceleration. The moment of inertia depends on the body’s mass and the distance from the axis of rotation, so again, higher head mass should result in lower rotational head accelerations. Indeed, both head mass and neck girth are inversely correlated with head acceleration in male and female collegiate soccer players (Mansell et al., 2005; Tierney et al., 2005, 2008). Increased neck girth is positively correlated with greater muscle tissue and may suggest higher neck stiffness resulting in an increase in effective mass and a lower head acceleration (Tierney et al., 2005). However, conclusions from these studies are limited in population (collegiate only). Herein, size (head mass, neck girth) predictors explained 22.1% of the variance in peak linear acceleration and 23.3% of the variance in peak rotational acceleration across 100 male and female soccer players ages 12–24. These data provide compelling evidence that we should consider anthropometric measurements when determining when an athlete can begin heading a soccer ball. Athletes with smaller head masses/neck girths may experience greater head impact magnitudes during soccer heading.