Unit of momentum

1. Jul 5, 2010

AJ Bentley

I was just trying to get my head around a point that was a little obscure, when I realised that part of the problem was that in thinking of momentum I hadn't got a name to hang on the unit.

Unlike energy, where you just think so-many-Joules or Force (ditto-Newtons), you get stuck with this clumsy kilogram-metres-per-second.

2. Jul 5, 2010

Dickfore

the atomic unit of momentum would be found by dimensional analysis from $m_{e}$. $\hbar$ and $k_{0} \, e^{2}$. The dimensions of these fundamental quantities are:

$$[ m_{e} ] = \mathrm{M}$$

$$[ \hbar ] = \mathrm{M} \, \mathrm{L}^{2} \, \mathrm{T}^{-1}$$

$$[ k_{0} \, e^{2} ] = \mathrm{M} \, \mathrm{L}^{3} \, \mathrm{T}^{-2}$$

The dimension of momentum is:

$$[p] = \mathrm{M} \, \mathrm{L} \, \mathrm{T}^{-1}$$

Assuming a general combination:

$$p = m_{e}^{x} \, \hbar^{y} \, (k_{0} e^{2})^{z}$$

we get the following conditions:

$$\left\{\begin{array}{l} x + y + z = 1 \\ 2 y + 3 z = 1 \\ -y - 2 z = -1 \end{array}\right. \Rightarrow \left\{\begin{array}{l} x = 1 \\ y = - 1 \\ z = 1 \end{array}\right.$$

Therefore, the atomic unit of momentum is:

$$p_{0} = \frac{m_{e} \, k_{0} \, e^{2}}{\hbar} = \alpha \, m_{e} \, c, \ \alpha \equiv \frac{k_{0} \, e^{2}}{\hbar \, c}$$

It's value in SI units is:

$$p_{0} = 1.99 \times 10^{-24} \, \frac{\mathrm{kg} \, \mathrm{m}}{\mathrm{s}}$$

Since Louis De Broglie found the relation between the wavelength and momentum, I propose the above unit be called broglie.

Last edited: Jul 5, 2010
3. Jul 5, 2010

AJ Bentley

I'd prefer something a little, well, 'snappier'...

4. Jul 5, 2010

Phrak

I suggest the Bentley. One kilogram meter per second is a Bentley.

5. Jul 5, 2010

AJ Bentley

Suck-up! :rofl:

6. Jul 5, 2010

Phrak

My original thought was the 'snappy', but with the tendency to name units after their discoverers....you did discover momentum didn't you?

7. Jul 5, 2010

I suppose Newton discovered the important features of momentum so let's stick with him and express momentum in Newton seconds(which is the same as kgm/s)

8. Jul 5, 2010

Phrak

That's an awfully nice tribute to Newton, but Newton-seconds doesn't have the ring to it one should expect from a basic quantity. Did Newton have a nephew, cousin, or anyone having a name with less than three syllables? You see, it’s never proper to use more than three syllables. All the best units are one, two, and never more than three syllables, I’d considered a Galileo, but poor Galileo has a name much too busy.

Last edited: Jul 5, 2010
9. Jul 5, 2010

Char. Limit

Since momentum is a quantity of motion, I suggest "motions".

"The automobile has about 60 kilomotions of momentum."

10. Jul 5, 2010

AJ Bentley

I can think of some other physical quantity you could name that way, that's much more appropriate!

'David Cameron today made a speech that registered at 15 kilomotions on the Bovine scale.'

Last edited: Jul 5, 2010