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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
Fuels and other energy sources
Published in Allan Bonnick, Automotive Powertrain Science and Technology, 2020
When a disc such as a flywheel is rotating, the whole of its mass may be considered to be placed in a ring at a radius that is the radius of gyration k (see Figure 9.11). The moment of inertia of a flywheel may be calculated from the formula I = mk2, where I is the moment of inertia, m is the mass of the flywheel in kg and k is the radius of gyration in metres. For a simple disc flywheel, the radius of gyration is k=r2wherer is the outer radius of the flywheel.
Transverse Vibrations of Simple Rotor Systems with Gyroscopic Effects
Published in Rajiv Tiwari, Rotor Systems: Analysis and Identification, 2017
The radius of gyration is an imaginary radius at which all the mass of the flywheel is assumed to be concentrated so as to have the same angular momentum as that of the actual flywheel. Now in the following section, we will investigate the gyroscopic moment in a disc and a propeller of a jet engine.
Impact of the seated height to stature ratio on torso segment parameters
Published in Ergonomics, 2020
Zachary Merrill, Charles Woolley, Rakié Cham
The mass of each segment was first calculated as the sum of the masses of the slices. Using the same assumptions as Ganley and Powers (2004), the centre of mass of each slice was assumed to be at its geometric centre, and the segments were modelled as sets of point masses along their longitudinal axes. Each segment centre of mass (COM) was calculated using the mass of each slice and its distance from the superior segment border to the slice’s centre of mass, summed and divided by the total segment mass. The moment of inertia about the superior border for each segment was determined with the slice masses and distances from the superior border, and the moment of inertia about the centre of mass was calculated from the moment of inertia, segment mass and centre of mass location using the parallel axis theorem. Finally, the radius of gyration (RG) was calculated as the square root of the moment of inertia about the centre of mass, divided by the segment mass. This process to determine the segment mass, centre of mass (COM) and radius of gyration (RG) was performed using a custom MATLAB script (Mathworks, Natick, MA, USA).
Thigh loaded wearable resistance increases sagittal plane rotational work of the thigh resulting in slower 50-m sprint times
Published in Sports Biomechanics, 2022
Paul Macadam, John B. Cronin, Aaron M. Uthoff, Ryu Nagahara, James Zois, Shelley Diewald, Farhan Tinwala, Jono Neville
where m = total segment mass, k = distance of the radius of gyration. The radius of gyration represents the object’s mass distribution with respect to a given axis of rotation. It is the distance from the axis of rotation to a point at which the mass of the body can theoretically be concentrated without altering the inertial characteristics of the rotating body. Due to the specific short lengths, the WR was placed at the end of the shorts, equivalent to approximately 80% distal from the hip joint centre as shown by the dashed line in Figure 2.