Units and Measurements

radian, steradian

Radian (rad) for plane angle and steradian (sr) for solid angle are the two supplementary units in SI system. Meter and kilogram are fundamental units, not supplementary.

Work, Heat, Force × Distance

Energy has dimensions [ML²T⁻²]. Work = Force × Distance = [MLT⁻²] × [L] = [ML²T⁻²]. Heat is also a form of energy. Power has dimensions [ML²T⁻³] and momentum has [MLT⁻¹].

6.4 × 10⁶ m

6400 km = 6400 × 10³ m = 6.4 × 10⁶ m. The number 6400 has 2 significant figures (since trailing zeros without decimal point are not significant), so we write 6.4 × 10⁶ m.

1/2

Let T ∝ l^a g^b. Dimensionally: [T] = [L]^a [LT⁻²]^b = [L^(a+b) T^(-2b)]. Comparing: a+b=0 and -2b=1, so b=-1/2 and a=1/2. Therefore, T ∝ l^(1/2).