Hurricanes can involve winds in excess of 100 km/h at the outer edge. Make a crude estimate of the energy of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 kg/m3) of radius 88 km and height 4.4 km .

Explanation:

We can approximate the hurricane as a rotating uniform cylinder, so its energy is the rotational kinetic energy, given by:

(1)

where

I is the moment of inertia

is the angular velocity

The moment of inertia of a cylinder rotating about its axis is

where

M is the mass

R is the radius

So formula (1) can be written as

(2)

For an object in rotation, the linear speed at the edge is related to the angular velocity by

So we can rewrite (2) as

where we have:

is the speed at the edge of the hurricane

We have to calculate the mass of the cylinder. We have:

(radius)

(height)

So the volume is

The density is

So the mass is

Therefore, the energy is

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