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When talking about a unit system, one thing to consider is that when you "set a constant to $1$", what you are really doing is expressing that constant in units such that the value of the constant is 1 (of those units). So, for example, $c = 299792458 \, \text{m}/\text{s}$, but if I choose units $d$ (distance) and $t$ (time) such that $1 d/t = 299792458 \, ...


In any unit system you want to define, you can set as many constants to 1 as you want so long as all of the constants are independent of each other. That is, the units for any one normalized constant cannot be obtained by manipulating the other normalized constants. That said, you cannot set numerical constants to 1. $\pi$ is always $3.141592.....$ because ...


Yes. Consider the equation for kinetic energy (KE): $${\rm KE} = \frac{1}{2} mv^{2}$$ the dimensions of KE are: $${\rm mass} \times {\rm velocity}^{2}=\frac{{\rm mass} \times {\rm length}^{2}}{{\rm time}^{2}}$$ or with SI units: $$1\,{\rm J} = 1\,{\rm kg}\,{\rm m}^{2}\,{\rm s}^{-2}$$


A slight expansion of the question: When a physical quantity in an equation is raised to a power (like being squared) then all the physical quantities that go into that quantity are also raised to the same power. So, velocity, $v$, has dimensions of length over time, $l/t$, and velocity squared, $v^2$, has dimensions of length squared over time squared, ...


Yes.The unit of $(\text{velocity})^2$ is $[\frac{\text{m}}{\text{s}}]^2$ .This is true for all calculations for any physical quantity.On squaring a physical quantity, its dimension gets squared. As a result, the unit is also squared.


Yes. If you square a variable, its unit of measurement is also squared, in the case of speed $v$ in $m/s$ ($ms^{-1}$), then $v^2$ is expressed in $m^2s^{-2}$. This is true for all physical variables (or constants).


The kilogram is the base unit of mass because electrical engineers in the late 19th century chose a particular set of practical electrical units. These practical units were a success, and we are still using them today: ohm, volt, ampere, and the joule. In 1874 the mechanical units cm, g, s ('CGS') were adopted as the coherent system of units for science. ...


The Sievert is a derived measure of stochastic health risk. It's used only in cases of low dosage ionizing radiation. High dosages that produce deterministic health effects are measured in the Gray (Gy), a purely physical term which represents the actual deposit of one joule of energy in one kilogram of matter. Unlike the Gray, the Sievert does not ...

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