The algebra of dimensionality, Physics

Assignment Help:

Rule 1: In order to sum or subtract two physical quantities the quantities must have the similar dimension. The final physical quantity has the similar dimensions. Physical quantities with the same dimension in different systems of units can be added or subtracted by multiplying one of the quantities by a unit conversion factor to get compatible units.

Rule 2: The product of two physical quantities results in a new physical quantity that has the sum of the exponents of the dimensions of the starting two quantities.

Rule 3: The division of one physical quantity by another results in a new physical quantity that has the dimension of the exponents of the first quantity minus the exponents of the second quantity.

Rule 4: Measuring the square root of a physical quantity results in a new physical quantity having a dimension with exponents half of the initial dimension.

Rule 5: The derivative of a physical quantity with respect to another physical quantity results in a new physical quantity with the exponents of the first dimension minus the exponents of the other dimension.

Example:  Speed v has dimension L/T, length l has dimension L, time t has dimension T, then dv/dt has dimension L/T2 of acceleration.

Rule 6: The integral part of a physical quantity over the range of one another physical quantity results in a new physical quantity that has a dimension with the sum of the exponents of the two quantities.

Example:  Speed v has dimension L/T, time t has dimension T, then integral v dt has dimension of length L.

 


Related Discussions:- The algebra of dimensionality

Illustrates quantum theory of black body radiation by planck, Illustrates t...

Illustrates the quantum theory of black body radiation by Planck? Planck’s quantum theory of black body radiation Planck was investigating the properties of light-emitting a

Draw and discuss pentode plate characteristics, Draw and discuss Pentode Pl...

Draw and discuss Pentode Plate Characteristics. Ans:  Pentode Plate Characteristics:   Pentode plate characteristics  (plate  current-plate voltage curves at constant grid vol

Draw a labelled diagram of an ac generator, Describe with the help of a lab...

Describe with the help of a labelled diagram the underlying principle and working of a step-up transformer. Why cannot such a device be used to step-up D.C. voltage? Or Dr

Polarization, Explanation construction and working of Nicol prism?

Explanation construction and working of Nicol prism?

A parallel plate capacitor each with plate area a, A parallel plate capacit...

A parallel plate capacitor, each with plate area A and separation d, is charged to a potential dissimilarity V. The battery used to charge it is then disconnected. A dielectric sla

Find the electric potential, Q. Find the electric potential at a distance 0...

Q. Find the electric potential at a distance 0.09 m from a charge of 4 X 10 -7 C. The electric potential V = ( 1/4πεo ) q /r = ( 9 X 10 9 X 4 X 10 -7 )/ 9 X 10 -2 = 4 X 10

Calculate the pressures at points, In this system, d = 6 in., D = 12 in., Δ...

In this system, d = 6 in., D = 12 in., Δz 1 = 6 ft, and Δz 2 = 12 ft. The discharge of water in the system is 10 cfs. Is the machine a pump or a turbine? What are the pressures a

Plot the engineering stress strain curves, Given the properties in the tabl...

Given the properties in the table below a. Plot the engineering stress-strain curves for the 3 materials. You can assume the materials behave linearly when they plastically

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd