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- Thread starter physics kiddy
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HallsofIvy

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Avogadro's number is the number of molecules

Plank's constant is the "h" in [itex]h\nu[/itex] where E is energy, and so has units of [itex]kg m^2/sec^2[/itex] while [itex]\nu[/itex], a frequency, is "number of cycles per second". "Number of cycles", like "number of molecules" is just a number without units. Since we need to have left "[itex]kg m^2/sec^2[/itex]" we need . That means that h must have units of [itex]kg m^2[/itex] in the numerator and one "sec" in the denominator: [itex]kg m^2/sec[/itex].

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Why is 1/2 in 1/2 mv^2 dimensionless ?

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Because mv^2 has the unit same as that of Energy.

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Please elaborate it mathematically.Because mv^2 has the unit same as that of Energy.

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[tex]C\cdot k\cdot \left(1\ \mathrm{J}\right)=k'\cdot\left(1\ \mathrm{J}\right)[/tex]

And so

[tex]C=\dfrac{k'}{k}[/tex]

And so C's dimensionless.

I wanted to point out that c, the speed of light, is dimensionless, equal to 1, in Special (and General, I'd imagine) Relativity. Basically, [itex]299792458\ \mathrm{m}=1\ \mathrm{s}[/itex].

I've always found it useful to think of units as constants that are, in some cases, incompatible with one another, so the simplest form is just their product.

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