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Linear and angular motion
Published in John Bird, Carl Ross, Mechanical Engineering Principles, 2019
The unit of angular acceleration is radians per second squared (rad/s2). Rewriting equation (15.9) with ω2 as the subject of the formula gives: ω2=ω1+αt where ω2 = final angular velocity and ω1 = initial angular velocity.
Head Injuries, Measurement Criteria and Helmet Design
Published in Youlian Hong, Routledge Handbook of Ergonomics in Sport and Exercise, 2013
Andrew Post, T. Blaine Hoshizaki, Sue Brien
Rotational (or angular) acceleration is the rate of change of rotational (angular) velocity over time, typically measured in rad.s−2. This dependent variable is not currently being used in most helmet standards. However, new and revised standards are considering changes to include this metric. The need to use rotational acceleration to evaluate helmets was established by researchers as far back as 1943 (Holbourn, 1943). In fact, it has been demonstrated that it is easier to create concussive and diffuse axonal type injuries than other types of TBI using a pure rotation. Holbourn (1943) demonstrated how important rotational motion is in identifying the risk of head injury from an impact. To date, helmets are only designed to manage peak linear acceleration, and in so doing primarily prevent injuries that are associated with these types of motion (Hoshizaki and Brien, 2004). As any impact can be quantified kinematically with linear and rotational acceleration, it would be useful to include both linear and rotational acceleration when evaluating the capacity of helmets to prevent head injuries. Thresholds of injury for mTBI using linear and rotational acceleration are presented in Table 33.1.
Pilot Control
Published in Pamela S. Tsang, Michael A. Vidulich, Principles and Practice of Aviation Psychology, 2002
An aircraft is a dynamic system whose motion in three-dimensional space is described by differential equations, obtained by application of Newton’s second law of motion. This law describes how the linear and angular accelerations of the aircraft depend on the applied forces and moments. A force is most easily described as a push or pull whereas a moment is a force applied through a distance or moment arm. Linear acceleration describes the rate of change of the linear velocity of the object’s center of mass, and angular acceleration describes the rate of change of angular velocity. The latter describes the rate at which the angular orientation of the aircraft is changing. The forces and the moments that an aircraft experiences can be categorized as aerodynamic, propulsive, and gravitational, with the first two being created by the aircraft’s motion through the atmosphere. The pilot modulates the aerodynamic and propulsive forces on the aircraft and thus controls the aircraft’s degrees of freedom and its movement in three-dimensional space. The aerodynamic forces are modulated through the deflection of aerodynamic control surfaces, such as the elevator, ailerons, and rudder. The propulsive forces are modulated through the control of fuel flow to the engine. See Fig. 8.2. The pilot effects these changes through manipulators in the cockpit, referred to as inceptors. In a typical cockpit, these inceptors consist of a column or wheel for elevator and aileron movement, foot pedals for rudder movement, and throttles to command fuel flow to the engine(s).
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.