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Introduction
Published in Vladimir A. Dobrushkin, Applied Differential Equations, 2018
where θ is an angle in the cylindrical coordinate system and in which the axis of rotation is taken to be in the z direction. The unit of angular velocity is a radian per second (rad/sec, which is 1/sec ) and it is a measure of the angular displacement per unit time. Since the velocity vector is always tangent to the circular path, it is called the tangential velocity. Its magnitude v=rdθ/dt=rω is the linear velocity, where r=|r| and ω=|ω|. In words, the tangential speed of a point on a rotating rigid object equals the product of the perpendicular distance of that point from the axis of rotation with the angular speed. Note that the tangential velocity and angular velocity only refer to its magnitude; no direction is involved. Although every point on the rigid body has the same angular speed, not every point has the same linear speed because r is not the same for all points on the object.
Introduction to Systems of ODEs
Published in Vladimir A. Dobrushkin, Applied Differential Equations, 2022
where θ is an angle in the cylindrical coordinate system and in which the axis of rotation is taken to be in the z direction. The unit of angular velocity is a radian per second (rad/sec, which is 1/sec) and it is a measure of the angular displacement per unit time. Since the velocity vector is always tangent to the circular path, it is called the tangential velocity. Its magnitude v=rdθ/dt=rω is the linear velocity, where r=|r| and ω=ω. In words, the tangential speed of a point on a rotating rigid object equals the product of the perpendicular distance of that point from the axis of rotation with the angular speed. Note that the tangential velocity and angular velocity only refer to its magnitude; no direction is involved. Although every point on the rigid body has the same angular speed, not every point has the same linear speed because r is not the same for all points on the object.
Introduction to Systems of ODEs
Published in Vladimir A. Dobrushkin, Applied Differential Equations with Boundary Value Problems, 2017
where θ is an angle in the cylindrical coordinate system and in which the axis of rotation is taken to be in the z direction. The unit of angular velocity is a radian per second (rad/sec, which is 1/sec) and it is a measure of the angular displacement per unit time. Since the velocity vector is always tangent to the circular path, it is called the tangential velocity. Its magnitude v=rdθ/dt=rω $ v = r{\text{d}}\theta /{\text{d}}t = r\omega $ is the linear velocity, where r=|r| $ r = |{\text{r}}| $ and ω=|ω| $ \omega = |{{\omega}} | $ . In words, the tangential speed of a point on a rotating rigid object equals the product of the perpendicular distance of that point from the axis of rotation with the angular speed. Note that the tangential velocity and angular velocity only refer to its magnitude; no direction is involved. Although every point on the rigid body has the same angular speed, not every point has the same linear speed because r is not the same for all points on the object.
Deciphering the interdependent impact of process parameters in friction stir welding - Part I: an overview of the challenges and way forward
Published in Materials and Manufacturing Processes, 2023
Simeon A. Babalola, Samik Dutta, Himadri Roy, Naresh C. Murmu
Where is the fractional slip; is the mechanical efficiency; is the shear yield strength; is the coefficient of friction; is the axial force; is the rotational speed; is the welding velocity. The term represents the tangential speed of the tool relative to the workpiece.[121] Although Eqn. (3) has a better depiction of the tool-plasticized BM interaction, quantifying the slippage parameter is not a trivial task. A seemingly better approach to quantify the process heat will be to estimate the peak temperature attainable during FSW. The peak temperature in the tool ambient influences the chances of producing a defect-free weld and the recrystallization/annealing activities that may occur in the BM. In this context, an estimate of the peak temperature () is[122–125]:
Modelling and control of a new differential steering concept
Published in Vehicle System Dynamics, 2019
In our case, the vehicle keeps track till the lateral acceleration becomes about (Figure 10). Further, self-steering properties of the vehicle might be concluded from this test. According to Figure 10(a), the vehicle shows understeering behaviour while with an initial self-steering gradient of about , and oversteering beyond. Certain characteristic values of vehicle speed may be obtained as well. For example, from Figure 10(b) we get for corresponding to tangential speed . The sideslip angle gain and yaw rate gain in Figure 10(c,f) are unbounded due to the oversteering characteristics. Figure 10(f) shows that the yaw rate gain goes to infinity at associated with critical speed . These results (except the oversteering behaviour) are typical for passenger cars [16].
Experimental investigation on the enhancement of Mode I fracture toughness of adhesive bonded joints by electrospun nanofibers
Published in The Journal of Adhesion, 2018
F. Musiari, A. Pirondi, A. Zucchelli, D. Menozzi, J. Belcari, T. M. Brugo, L. Zomparelli
The solution is injected in a needle, kept under high voltage by a power supply. Therefore, it is subjected to an electric field, which induces, in turn, an electric charge on the solution surface. When the electric field attains a threshold, the repulsive electric forces overcome surface tension, resulting in flash evaporation of the solvent and polimerisation of the nylon in the first millimeters after the exit from the needle. The liquid-solid polymer filament is accelerated and whirled around by electric forces during the travel between the needle and the grounded (null electric potential) rotating drum, Figure 1. The electrospinning parameters were as follows: 1) applied voltage: 24 kV; 2) needle inner diameter: 0.8 mm; 3) needle collector distance: 15 cm; 4) feed rate: 0.3 ml/h per nozzle; 5) environment: humidity at 40% and room temperature (23°C). Tangential speed of the collecting drum: 0.2 m/s.