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

Nominal resistance, The resistances of commercially-available discrete resi...

The resistances of commercially-available discrete resistors are restricted to particular sets. For example, the available values of resistors with 10% tolerance are selections fro

Kinematics.., As we''re on an inclined plane shouldn''t we take the x & y c...

As we''re on an inclined plane shouldn''t we take the x & y components of gravity into consideration?? thanks

Microwave Radiative Transfer in the Atmosphere, I''m transmitting microwave...

I''m transmitting microwave radiation from antenna to satellite..so when radiation(photons) is transmitted,how they interact with the molecules in the atmosphere layer by layer..I

Honors, an orchestra tunes up for the big concert by playing an A, WHICH RE...

an orchestra tunes up for the big concert by playing an A, WHICH RESOUNDS WITH A FUNDAMENTAL FREQUWNCY OF 440HZ FIND THE SECOND AND TIRD HARMONICS OF THIS NOTE

Explain the transmission of heat, Explain the Transmission of Heat Tran...

Explain the Transmission of Heat Transmission of heat (movement of heat from the hotter item to the colder item) can be brought about three ways: by conduction, convection, and

Laser, what is the importance of laser?

what is the importance of laser?

Electrostatic, two insulated charge Cu spheres A and B OF IDENTICAL size ha...

two insulated charge Cu spheres A and B OF IDENTICAL size have charge qa and -3qa when they are brought in contact with each other and separated,what are new charge on them

Steps of working of unijunction transistor, Steps of working of Unijunction...

Steps of working of Unijunction Transistor (i)  When emitter circuit is closed through switch S but emitter voltage is reduced to zero, and a voltage V BB is applied between

Hoop conjecture, Hoop conjecture (K.S. Thorne, 1972): The conjecture (...

Hoop conjecture (K.S. Thorne, 1972): The conjecture (as still unproven, though there is substantial evidence to hold up it) that a nonspherically compressed, nonspherical obje

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