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Coriolis Acceleration and Force in Mechanical Engineering

In Mechanical Engineering the Coriolis acceleration is a component of acceleration experienced by a particle which is part of a rotating member. The acceleration occurs when a particle is constrained to move radially with respect to a rotating part. In the illustration an element of mass m at radius r moves radially with speed v along a rotating arm having angular velocity w. The Coriolis acceleration is 2wv or 2w dr/dt, while the centripetal acceleration is rw^2. The directiions of the accelerations are as shown. Note that the accelerations are relative to a fixed, non-rotating reference frame. If the sliding element has mass m, then the rotating arm must exert forces 2mwv and mrw^2 in the same directions as the accelerations. These forces may lead to mechanical failure of the rotating part if it is not sufficiently strong to withstand them. The forces are the Coriolis Force and the centripetal force respectively. The latter force is reacted to by the Centrifugal Reaction.

Electrical

A signal traveling along an electrical transmission line can be partially or fully reflected at a discontinuity or impedance mismatch - for example at a point where a load whose impedance (Z_{\mathrm {L} ) differs from the characteristic impedance of the line (Z_{\mathrm {0} ) The ratio of the amplitude of the reflected wave Vr to the amplitude of the incident wave Vi is known as the reflection coefficient {\displaystyle \Gamma }.

{\displaystyle {\mathit {\Gamma }}={V_{\mathrm {r} } \over V_{\mathrm {i} }}} = \Gamma ={Z_L-Z_0 \over Z_L+Z_0}

{\displaystyle \Gamma } is related to the

When the source and load impedances are known values, the reflection coefficient is given by

{\displaystyle {\mathit {\Gamma }}={{Z_{\mathrm {L} }-{\bar {Z}}_{\mathrm {S} }} \over {Z_{\mathrm {L} }+Z_{\mathrm {S} }}}}

where ZS is the impedance toward the source and ZL is the impedance toward the load. Note that this formulation for Gamma is inconsistent with the formulation expressed in the entry for Reflection Coefficient and cannot be used to calculate the Voltage Standing Wave Ratio.

Return loss is the negative of the magnitude of the reflection coefficient in dB. Since power is proportional to the square of the voltage, return loss is given by,

{\displaystyle RL(\mathrm {dB} )=-20\log _{10}\left|{\mathit {\Gamma }}\right|}

where the vertical bars indicate magnitude. Thus, a large positive return loss indicates the reflected power is small relative to the incident power, which indicates good impedance match between transmission line and load.

If the incident power and the reflected power are expressed in 'absolute' decibel units, (e.g., dBm), then the return loss in dB can be calculated as the difference between the incident power Pi (in absolute decibel units) and the reflected power Pr (also in absolute decibel units),

{\displaystyle RL(\mathrm {dB} )=P_{\mathrm {i} }(\mathrm {dB} )-P_{\mathrm {r} }(\mathrm {dB} )\,}