Dimensional analysis is a powerful verification and derivation tool.

Key Dimensions:

Applications:

1. Verify equations: All terms must have same dimensions. E.g., v = u + at: [$LT^{-1}$] = [$LT^{-1}$] + [$LT^{-2}$][T] = [$LT^{-1}$]. Correct.
2. Derive relations: If T depends on l and g: [T] = [L]^a[$LT^{-2}$]^b gives a+b=0, -2b=1, so b=-1/2, a=1/2. T = k*sqrt$\frac{l}{g}$.
3. Detect errors: If dimensions don't match, the equation is definitely wrong.

Limitation: Cannot determine dimensionless constants (like 2*pi) or distinguish between dimensionally identical quantities.