New answers tagged

1

Of course, you can do it with Matlab, Mupad, Maple, Mathematica or even the Smart Math Calculator. Use this method: First define your variables with your units of choice, then tell the programm what the conversion factors from the given units to the target units are, for example, if you have km/h and need m/sec define 1km as 1000m and 1sec as h as 60² ...


2

From the paper, which states fiber Bragg gratings (FBG) have been demonstrated to exhibit temperature dependent shifts in resonant wavelength of 10 pm/K it is fairly clear that the unit is picometer per kelvin. That is, you have some device with a resonance wavelength $\lambda_\mathrm{R}$ which depends on temperature, ...


1

Few of the answers thus far have directly addressed empirical equations, such as the following: Vapor pressure of isobutane (source) $$ \log_{10}{P_\mathrm{mmHg}}=6.74808-{882.80\over 240.0+T_\mathrm{^\circ C}} $$ Seeton model for kinematic viscosity of various liquids (source; $K_0$ is the zero-order modified Bessel function of the second kind) $$ ...


1

As mentioned by the other answers, it is the dimension which essentially needs to be the same on both sides of an equation and not the unit. This has already been spoken with the example of $1 \,\mathrm{hour} = 60 \,\mathrm{minutes}$. Let me give you one example and illustrate to you that: The thing called unit has been merely developed for our own ...


10

It's worth noting natural unit systems, which may appear to violate this rule. Since certain physical constants (e.g., $G$ and $c$) simply reflect an arbitrary choice of units, it can be convenient to change units so that they are identically 1. For example, in Planck units, where $G=c=1$, we can write the Schwarzschild radius as $r_s = 2m$. While it ...


5

There is a simple argument to see why dimensions must agree on both sides. To use innisfree's example, consider the (obviously wrong) equation $$m_e = c\tag{*}$$ $m_e$ being the mass of the electron and $c$ the speed of light. I assume I have written this equation in the International System units (kilograms, meters, seconds). Now if I want to write this ...


15

No. All equations have the same dimension on both sides. Dimensions are mass, distance, time, speed, acceleration, force, power, electric current, electric charge etc. As long as you work with symbolic relations, you only care about dimensions. The equation $$v = \frac{s}{t}$$ (velocity = distance / time) works with any units as long as they are units for ...


33

It depends what you mean by "unit". If you mean something like "seconds", then no. Counterexample: 1 minute = 60 seconds has different units on both sides, but they're both representing a duration, so they can still be equal. If you mean something like "time", then yes. An equation means two things are equal, i.e. the same. For that to be true, they have ...


8

They have to be equal, because if the units are not identical, we will add fudge factors to make them identical. What you are looking at is called dimensional analysis. Dimensional analysis is a tool that lets us turn equations like $x(t) = \frac{1}{2}at^2 + vt + x_0$ into something meaningful in the real world. The real truth is that there are no "units" ...


1

Hint: what do you get if you add two apples to three oranges? You can only add like things to like things. In this sense it is technically correct to add 1 m to 3 inches and quote the result as 1 m 3 inches (both are measurements of lengths), but it would not be very useful or good practice. There are seven fundamental units: kilogram, metre, candela, ...


17

The dimensional units in an equation must balance. Sometimes a dimensionless "unit" may appear on one side and not be obvious (or even present) on the other side. For example, consider the kinetic energy of a spinning object: $$K_s = \frac{1}{2}\mathcal{I}\omega^2.$$ A comparison of SI units yields the following: $$[J]=[kg\cdot m^2]\frac{[rad]^2}{[s]^2}$$ ...


3

Yes for sure. After all you cannot say 5 chickens = 2 buffaloes. Here is an excerpt from NCERT physics for class 12 Chapter 2. I hope this helps. The recognition of concepts of dimensions, which guide the description of physical behaviour is of basic importance as only those physical quantities can be added or subtracted which have the same dimensions. ...


82

It doesn't matter where the equation came from - a fit to experimental data or a deep string theoretic construction - or who made the equation - Albert Einstein or your next-door neighbour - if the dimensions don't agree on the left- and right-hand sides, it's nonsense. Consider e.g. my new theory that the mass of an electron equals the speed of light. It's ...


7

Every equation should have corresponding dimension. Either by the natural dimensions of the equation $$\text{Average Speed} = \frac{\text{Distance}}{\text{Time}}$$ or by some constant which gives the correct dimension $$F = \frac{Gm_1 m_2}{r^2}$$ Where $G$ has dimension $[M^{-1}] [L^3] [T^{-2}]$ to ensure that the dimensions are equal on both sides.


1

Suppose you take a circle of radius $\ell$ and take an arc of length $\ell$ along the circumference, then 1 radian is the angle subtended by the arc: More generally, if the length of the arc is $\ell$ and the radius of the circle is $r$ then the angle in radians subtended by the arc is $\ell/r$. So the radian is a derived unit because it is the ratio of ...


0

http://www.britannica.com/science/electromagnetic-unit-of-charge electric charge Electric charge ...× 10−19 coulomb. In the centimetre–gram–second system there are two units of electric charge: the electrostatic unit of charge, esu, or statcoulomb; and the electromagnetic unit of charge, emu, or abcoulomb. One coulomb of electric charge equals about ...


0

The counting is done by the signal generator. The clock contains a signal generator that generates the 9,192,631,770 Hz signal going to the microwave transmitter. This generator contains a counter that counts every cycle the generator creates (though as The Photon says it may use a prescaler).


1

Nowadays it's reasonable to make an actual digital counter that operates at 10 GHz. Even so, you might rather use a prescaler to divide this frequency down to 1/4 or 1/8 of the microwave frequency before you actually start counting cycles. In olden times you might have generated your 10 GHz signal by multiplying up a lower frequency (maybe in the 100's of ...


0

Yes, it would be right; and this definition even coincides with the normally used definition. It would be right also to define the unit "fekaok" which is the force which accelerates the actual mass of your body by $1.337\,$ms$^{-2}$. This would be a good force definition as well, but not be equal to one Newton.


1

The kgwt is not a unit which you should be using rather use the newton (N) as the unit of force. 9.8 crops up in a number of situations. The force of gravitational attraction on a mass of 1 kg on the Earth is 9.8 N. Another way of putting that is that the gravitational field strength on the surface of the Earth is 9.8 N/kg. The acceleration due to ...



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