# Homework Help: The dimensions of something please

1. Jun 8, 2012

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

$$\frac{\omega c}{\sqrt{G}}$$

Would I be right in saying this has dimensions of force?

Thank you!

2. Jun 8, 2012

Oh, omega is angular frequency, I believe. c is the speed of light and G is newtons constant.

3. Jun 8, 2012

### Muphrid

The dimensions of force are mass times length over time squared; let's call that $F = ML/T^2$. Velocity is $v = L/T$. What would frequency be, then, and the square root of the gravitational constant?

4. Jun 8, 2012

So, what I have is angular frequency times the speed of light over the gravitational constant, so what you are saying is that

$$F \ne \frac{\omega c}{\sqrt{G}}$$

?

5. Jun 8, 2012

### Muphrid

I haven't said anything of the kind. I'm asking you what the dimensions are of $\omega$ and $G$. The first one should be easy; the second might be a little harder, but as a hint, use Newton's force law for gravitation.

6. Jun 8, 2012

I am still learning this dimension stuff, so don't expect me to be overly useful.

Newtons force law is mass x m/s/s yes? So how does this help me? I don't know the dimensions to angular frequency... is it just a frequency?

I see one link saying it is M^0L^0T^-1

so what is this for frequency, just 1/time? So how will this help me? I don't even know how to calculate terms like these together?

7. Jun 8, 2012

G just has dimensions of speed squared? Or that was what someone told me once. Is that true?

8. Jun 8, 2012

### Muphrid

Frequency is 1/time, yes.

Newton's law of gravitation is $F = Gm_1 m_2/r^2$ In the language of dimensions, that's force = G x (mass) x (mass) / (length x length). Knowing the dimensions of force already, you should be able to solve for the dimensions of G.

9. Jun 8, 2012

I'm clueless how to. I don't know how you calculate terms... I can solve for G... that is easy...

$$Fr/m^2 = G$$

So.... now what?

10. Jun 8, 2012

### Muphrid

That's $r^2$.

You need to plug in the dimensions of force now.

11. Jun 8, 2012

Sorry, treat for r^2. Forgot that... now what do you mean I need to plug in for force? I am alien to this... helping me with a working example would be much more educational for me... This is total chinese for me.

12. Jun 8, 2012

### Muphrid

You measure lengths in meters. You measure time in seconds and mass in kilograms. You measure force in newtons, where 1 newton = 1 kg m/s/s.

Take what you just wrote:

$F r^2 /m^2 = G$

And convert it to units. "Force -> newtons" for instance. $r^2$ -> meters squared, and so on.

$(\text{newtons}) (\text{meters})^2 / (\text{kilograms})^2 = G$

But you know that newtons can be expressed in terms of kilograms, meters, and seconds, right?

13. Jun 8, 2012

right... I think I am following... now?

14. Jun 8, 2012

How do you calculate something like

Newtons x meters^2

I need to be shown before I can do it.

15. Jun 8, 2012

### Muphrid

Newtons = kilograms x meters / (seconds)^2

16. Jun 8, 2012

Then how would you divide it by kilograms^2... I would believe there is some kind of special conversion formula to get from newtons to the rest right?

17. Jun 8, 2012

### Muphrid

It's perfectly fine to leave one power of kilograms in the denominator.