# Homework Help: Still learning dimensional analysis

1. Jul 24, 2012

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

angular frequency omega, speed of light and gravitational constant

2. Relevant equations

Just the expression,

$$\frac{2 \omega c}{\sqrt{G}}$$

3. The attempt at a solution

Still learning dimensional analysis. So I am simply wanting to know if I have done this right. If I have, I get

$$\frac{2 \omega c}{\sqrt{G}}$$

this with dimensions of force, right?

2. Jul 24, 2012

### cepheid

Staff Emeritus
Re: dimensions

I'll use square brackets around a quantity to mean, "dimensions of" that quantity (which is a fairly common notation, I think). Then:

[ω] = time-1

[c] = length * time-1

[√G] = [G]1/2 = (force * length2 * mass-2)1/2

Therefore [ωcG-1/2] = length * time-2 * force-1/2 * length-1 * mass

= force-1/2 * mass * time-2

= (mass * length * time-2)-1/2 * mass * time-2

= mass1/2 * length-1/2 * time-1

So, no, it doesn't have dimensions of force.

3. Jul 26, 2012

Re: dimensions

What does it have dimensions of then? I mean, other than what you have said, is there a commonly known dimension it exhibits? like energy for instance?

4. Jul 26, 2012

### cepheid

Staff Emeritus
Re: dimensions

It doesn't correspond to any common physical quantity, and there is no reason that it has to (you've simply come across a new type of quantity),

However, the *square* of the quantity is a common type of quantity. Hint: square everything in blue, and rearrange things to produce "force" plus some leftover stuff. What is the dimension of the quantity you've come up with?