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Published in Splinter Robert, Illustrated Encyclopedia of Applied and Engineering Physics, 2017
[general, mechanics, quantum] (rad/s) The rate of change in angular position with respect to a reference frame or fixed point for an object moving in curved trajectory; the definition of angular velocity is ω=dθ/dt. This angular velocity is constant for every point in uniform circular motion, since the rate of change in angular position is independent of the distance to the origin. The angular velocity also relates to the hypothetical circular orbit of the time-dependent sinusoidal amplitude of an alternating signal, which repeats every 2π or one period. Examples of waves with a sinusoidal pattern are electromagnetic radiation and sound. The tangential velocity (v) of a point in circular motion will increase with distance (r) to the axis as: v = tω
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.
Modification of the cyclone separator geometry for improving the performance using Taguchi and CFD approach
Published in Particulate Science and Technology, 2019
S. Venkatesh, M. Sakthivel, S. Sudhagar, S. Ajith Arul Daniel
The Figure 6 shows the contours of tangential, radial and axial velocity of standard cyclone separator. From this contour plot, it is identified that the maximum tangential velocity is 28.2 m/s, axial velocity is 7.54 m/s and the radial velocity is 3.34 m/s. The Figure 7 shows the contours of tangential, radial and axial velocity of new design cyclone separator. From this contour plot, it is identified that the maximum tangential velocity is 18.6 m/s, axial velocity is 6 m/s and the radial velocity is 3.4 m/s. The tangential and axial velocity of new cyclone is least when compared with the standard one. Also, these velocities gradually reduced at the mid portion of the cylinder which is blue in colour for both the standard and new designs. The radial velocity is maximum around the vortex finder region for both designs.