Global Journal of Science Frontier Research: A Physics and Space Science Volume 15 Issue 1 Version 1.0 Year 2015 Type : Double Blind Peer Reviewed International Research Journal Publisher: Global Journals Inc. (USA) Online ISSN: 2249-4626 & Print ISSN: 0975-5896 Formulate Equations for Reciprocity Vector and Scalar of Some Mechanical and Electrical Quantities By Faisal A. Mustafa Babylon University, Iraq Abstract- This study deals a new concepts of some physical reciprocally quantities which are vectors or scalars and its relationship with the fundamental quantities. The reciprocal of kinematics dimension quantities of moved particle for linear, rotational and circular movement are resulted the quantities that so called the time quantities such as time velocity, time acceleration. Other derivative quantities were derived from the principle equations to produce reciprocal movement equations. For dynamical mechanics, the quantities were derived from the principle equation such as time force, momentum, torque, energy,…ect. Also some reciprocal quantities due to electricity equations include the reactance, electric current, conductivity, …ect, and its derivative quantities are introduced time current density, time power. Keywords: reciprocal of velocity, conductivity, reciprocal current , inverse quantity, reciprocal , time electric field. GJSFR-A Classification : FOR Code: 240402 FormulateEquations forReciprocityVectorandScalarofSomeMechanicalandElectricalQuantities Strictly as per the compliance and regulations of : © 2015. Faisal A. Mustafa. This is a research/review paper, distributed under the terms of the Creative Commons Attribution- Noncommercial 3.0 Unported License http://creativecommons.org/licenses/by-nc/3.0/), permitting all non commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. Formulate Equations for Reciprocity Vector and Scalar of Some Mechanical and Electrical Quantities Faisal A. Mustafa Abstract - This study deals a new concepts of some physical special relativity as a complete tools[3].( Mushfiq,2012) reciprocally quantities which are vectors or scalars and its have observed a reciprocal relation between Planck's 2015 relationship with the fundamental quantities. The reciprocal of hypothesis and Einstein's postulate (special relativity). kinematics dimension quantities of moved particle for linear, r Particle velocity and de Broglie wave velocity are also ea rotational and circular movement are resulted the quantities Y that so called the time quantities such as time velocity, time reciprocally related[4].The longitudinal component of the acceleration. Other derivative quantities were derived from the velocity of a particle at or near a glacier surface, its 45 principle equations to produce reciprocal movement position is a function of time being term its trajectory equations. For dynamical mechanics, the quantities were velocity distribution are studied by (L.A. Rasmussem, derived from the principle equation such as time force, 1983)[5].The reciprocal relation give a correspondence momentum, torque, energy,…ect. Also some reciprocal between discrete and continuous quantities[4]. quantities due to electricity equations include the reactance, Movement constitutes a set defined by intrinsic V I electric current, conductivity, …ect, and its derivative relativity, reciprocity, and simulation of translation and quantities are introduced time current density, time power. The ue ersion I s rotation of all moving entities, the soveons. Soveon, s results show that the concept of reciprocal of some quantities I describes the quantity from two faces, first the principle elements and subsets, have angular and linear X quantities as were known, which depend on time and second velocities[6]. XV the reciprocal of this quantity, that independent on time and In pure geometry the theories of similar gives a new concept to the same quantity, describe the motion (reciprocal theorem of Betti and Raleigh) reciprocal and of particle or field. This will add a complete meaning of inverse figures (reciprocal diagram) have led to many movement of a particle, if a particle is a moving neutral or extensions of science (e.g. the refractive index being ) charged particle, or intrinsic quantity. A proportional to the velocity or the reciprocal of velocity) ) Keywards: reciprocal of velocity, conductivity, reciprocal [7] Attenuation coefficient is measured using units of . current, inverse quantity, reciprocal, time electric field. reciprocal length. If the capsular theory was taken, it will use the reciprocal of velocity as a multiplier instead of I. Introduction the velocity itself. For simplicity, the variability of the time Research Volume t(x) is elapsing between timing events, but the time ost the physical laws are dependant on time. velocity and reciprocal of velocity are the same[8] The The concept of the reciprocally physical concepts generalize to time - varying and to vector – Frontier Mquantity, gives another meaning, but with the valued Morse functions [9]. It sometimes uses the same concept of moving particle or group of particles, reciprocal lattice for crystal structure. It should now be for example: the reciprocal of velocity for kinematics ( clear that the direct lattice, and its reticular planes, are with no inertia) and for dynamics movement give directly associated (linked) with the reciprocal lattice. Science another concept. (Mushfiq, 2009) defined as well (Lima Siow) formulated equivalent principle that the of slowness ὐ as reciprocal of υ ; ὐ = 1/ υ = t / x, therefore, kinetic acceleration is equal to the potential acceleration objectivity demands that motion described in terms of (d2r/ dt2= - dΦ/dr) [10] Lorson explains, in the equation of slowness that should be as valid as the description in motion, time is the reciprocal of space and space is the Journal terms of velocities, its postulate in kinematics is reciprocal of time. This leads to a new concept of symmetry under reciprocal inversion of velocities or the motion, which Larson calls scalar motion. Larson,s idea Global motion is invariant under inversion υ → 1 / υ and vice that time and space are reciprocals is difficult to versa [1]. Slowness must form a group, difference understand in the context of the conventional space – between two slowness is slowness, therefore slowness time framework as if to say that the march of time is the must be discrete[2]. ( Md Shah Alam, et al.2005) reciprocal of extension space, which we ordinarily think Applied the mixed numbers algebra( sum of scalar and of as a container of matter. It is much easier to grasp vector) in quantum mechanics, electrodynamics and when we considers a theoretical universe of motion in which the only significant physical quantity is the Author: Laser Physics Department/College of Science for Women, magnitude of that motion, measured as speed or Babylon University-Iraq. e-mail:[email protected] velocity [11]. ©2015 Global Journals Inc. (US) Formulate Equations for Reciprocity Vector and Scalar of Some Mechanical and Electrical Quantities As noted earlier, in the RST's (reciprocal state of scalar, thus the reciprocal of any scalar quantity (P) is time) postulated three-dimensional motion, three- equal to another concept of the scalar quantity or: ( Q ) dimensional time-motion is the inverse of three- 1 dimensional space-motion. But it is important to Q = (3) remember that space-motion has no direction in time, P just as time-motion has no direction in space. Likewise, Equation 3 can be applied to any physical in the equation of time-motion, v' = t/s, t has direction in scalar quantity by taken its reciprocity. time, but s has no direction in time and is a scalar value. Larson summarizes this concept as follows: In the a) Reciprocal of Some Physical Quantities equations of motion in space, time is scalar. In the i. The Reciprocal of Velocity equations of motion in time, space is scalar and In the It states that the reciprocal of kinetic dimension equations of motion in space-time, both space and time velocity is equal to the gradient of time or time velocity, are scalar. However, in certain situations they are which conventionally is expressed as [12]: 2015 distinguished, as follows[11]. The term reciprocal refers r to the key concept of the RST that reflects the ^ Yea u postulated relationship of space and time as reciprocals −= d tgra (4) 46 of each other in the definition of motion. This strict study vr does shed more light into understanding the basic conceptual and theoretical framework on which the ∧ ∂t ∧ ∂t ∧ ∂t or − x + y + z Where the R.H.S. of the concepts are more complicated to other fields of ∂x ∂y ∂z physics. The moving phenomenon of particle are V equation is equivalent to I described from two sides dimensionally and timely which have a second new formulas for mechanical and ^ ue ersion I → s u s electrical equations. From the practical point of view, it is −= I v (5) important because it provides techniques, which can be t vr X XV used in almost any areas of pure and applied researches due to motions. such that û is a unit vector of νr or νt and the absolute value of equation (5) leads to the formula ν = 1/ν r t II. Theoretical The negative sign of eq. (5) is placed to compare two or more numerical values of particle ) A Suppose y is a physical vector quantity, and y velocity. In other wards the negative numerical value ) x t is the reciprocity, so physical quantity vector is equal to decreases as number increase. The variable ν is t the reciprocal of another quantity which have the same defined as the reciprocal of dimension velocity or direction and another concept of the same phenomena velocity of time in any units (in units: scm-1, sm-1, or -1 Research Volume movement: μskm ,…). The change of the time speed or velocity per ∧ → x unit displacement of an object give us another concept y −= (1) of acceleration called time acceleration. Frontier x yt To evaluate the time acceleration, multiply eq. ∧ (4) by the grad operator this yields[11]: is the unit vector of the quantity yt .