Rotational motion. one problem. Hurricanes can involve winds in excess of 120km/h at the outer edge.?

Question

Hurricanes can involve winds in excess of 120km/h at the outer edge. Make a crude estimate of

(a) the energy, and

(b) the angular momentum, such as hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3kg/m^3) of radius 100km and height 4.0 km.

Answer 1

I = (1/2)mr^2

m = ρπhr^2

K.E. = (1/2)((1/2)(ρπhr^2)r^2)ω^2

K.E. = (1/4)(ρπhr^4)(v/r)^2

K.E. = (1/4)(ρπhr^2)(v^2)

K.E. = (1/4)(1.3 kg/m^3)(π)(4,000 m)((100,000 m)^2)(((120,000 m/h)(1 hr/3,600 s))^2)

K.E. ≈ 4.537856e+16 J

P = (1/2)(1.3 kg/m^3)(π)(4,000 m)(100,000 m)^3)(120,000 m/h)(1 hr/3,600 s)

P ≈ 2.094395e+20 kgm/s