[How would I check a formula for dimensional consistency? e.g., T= 2π √L/G is the formula for a single pendulum to complete a single oscillation.
T = Time to complete oscillation
L = Length of the pendulum
G = Acceleration due to gravity

Question

[How would I check a formula for dimensional consistency? e.g., T= 2π √L/G is the formula for a single pendulum to complete a single oscillation.
T = Time to complete oscillation
L = Length of the pendulum
G = Acceleration due to gravity

aum · Answer

2 and π are dimensionless and so we don't have to worry about it.
$$
\sqrt{\frac LG } = \sqrt{\frac {m}{m/s^2}} = \sqrt{s^2} = s 
$$

aum · Answer

Right hand side reduces to seconds (or time) and the left hand side is Time period in seconds.  So they formula is dimensionally consistent.

anonymous · Answer

Wow. You actually made this make sense to me. I completely understand it now. Thanks so much!

aum · Answer

You are welcome.  Glad to be able to help.