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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).
Linear and angular motion
Published in W. Bolton, Higher Engineering Science, 2012
For the linear motion of the centre of mass of the sphere, the forces acting parallel to and down the plane are: mg sin θ−F=ma where a is the linear acceleration down the plane and F is the frictional force. As the sphere descends it rotates about its centre. The torque giving this rotation is that due to the frictional force and is thus Fr, where r is the radius of the sphere. Thus: Fr=Ia where a is the angular acceleration of the sphere. The moment of inertia I of the sphere is 2mr2/5. Thus: Fr=25mr2×a
Engineering Mechanics
Published in P.K. Jayasree, K Balan, V Rani, Practical Civil Engineering, 2021
P.K. Jayasree, K Balan, V Rani
The radius of gyration indicates the distribution of the components of an object around an axis. In terms of the mass moment of inertia, it is measured as the perpendicular distance from the axis of rotation to a point mass (of mass, m) which gives an equivalent inertia to the original object (of mass, m). Mathematically, the radius of gyration is the root mean square distance of the parts of the object from either its center of mass or a given axis. The radius of gyration is given by the following formula: k=IA
Evaluation of maximum thigh angular acceleration during the swing phase of steady-speed running
Published in Sports Biomechanics, 2023
Kenneth P. Clark, Laurence J. Ryan, Christopher R. Meng, David J. Stearne
Finally, the findings of this study may provide insight into optimal strategies for training interventions. Angular acceleration is proportional to torque and inversely proportional to the moment of inertia due to Newton’s second law for rotation. Thus, the functional capability to produce the larger angular acceleration values required at higher speeds is largely determined by the runner’s maximum torque capacity at the hip joint. This concept is supported by research demonstrating that measurements of hip flexion power and moments are positively related to sprinting speed (Copaver et al., 2012; Nagahara et al., 2020). Therefore, interventions aimed at improving an athlete’s hip torque capacity (and thus maximum thigh angular acceleration), such as resistance training to increase hip flexor strength (Deane et al., 2005) or use of wearable resistance during sprinting (Macadam et al., 2020), may be warranted.
Athlete body composition influences movement during sporting tasks: an analysis of softball pitchers’ joint angular velocities
Published in Sports Biomechanics, 2022
Kenzie B. Friesen, Arnel Aguinaldo, Gretchen D. Oliver
Regarding the SPM MANOVA analysis (Figure 3), results revealed slight differences in joint angular velocities between the two groups of pitchers. The observed differences seemed to have occurred surrounding the two events of ball release and follow-through, specifically at 74–75% and 92–99% of the phase under examination. Of note, ball release occurred at 77% of this phase, therefore differences occurred just prior to the ball release event, and then again just prior to the follow-through event. The main theoretical difference between these two groups of pitchers is the presence of additional body fat among the ‘high-fat’ group of pitchers. Since the pitchers within the high-fat% group are typically larger, they will have an increased segmental mass moment of inertia. Mass moment of inertia is the measure of a segment to resist change in angular velocity and is calculated as the product of the mass of a segment and the radius of gyration squared. Therefore, as taller and heavier pitchers exhibit longer and heavier arms, the segmental mass moment of inertia is increased. Hence, if both groups of pitchers applied the same torque to rotate segments, pitchers with heavier segments would achieve lower angular accelerations. With segments changing speed at a slower rate, they may need more time to achieve the intended body position. As a result, it was hypothesised that high-fat% pitchers would have altered joint motion through the pitch.
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.