Dimensional Analysis Explained - MIT 8-01

[Aspchizo]

In http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-1/ at about 23 minutes in, he starts talking about dimensional analysis. Can someone help expand on this a bit? I don't understand the Alpha, Beta and Gamma terms he uses.

Thanks.

 

[grzz]

The professor is making the assumption that the time t of fall of an object depends on the height h from which it falls, the mass m of the object and the acceleration g due to gravity.

He is using dimensional analysis to derive the required formula.

The powers of h, m and g are still unknown. Hence he is using the symbols $\alpha$,$\beta$ and $\gamma$ for these powers.

 

[Aspchizo]

So they are just algabraic placeholders?

 

[grzz]

The $\alpha$.$\beta$ and $\gamma$ are, as yet, unknown values to be determined later by equating the dimensions on each side of the resulting equation.