Hurricanes can involve winds in excess of 120 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*m^3 of radius 120 km and height 4.5 km.

Make a crude estimate of the angular momentum of such a hurricane.

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To estimate the energy of a hurricane, we can assume it as a rigidly rotating uniform cylinder of air and use its kinetic energy formula. The kinetic energy of an object can be calculated using the formula:

KE = 0.5 * I * ω^2

Where:
KE is the kinetic energy
I is the moment of inertia
ω is the angular velocity

To estimate the angular momentum of a hurricane, we can use the concept of conservation of angular momentum. The angular momentum of an object is given by the formula:

L = I * ω

Where:
L is the angular momentum
I is the moment of inertia
ω is the angular velocity

Let's calculate both the energy and angular momentum of the hurricane using these formulas.

Step 1: Calculate the moment of inertia (I)
The moment of inertia of a cylinder can be calculated using the formula:

I = 0.5 * M * R^2

Where:
M is the mass of the cylinder (density * volume)
R is the radius of the cylinder

To find the mass (M), we can calculate the volume of the cylinder:

Volume = π * radius^2 * height

Given:
Density (ρ) = 1.3 kg/m^3
Radius (R) = 120 km = 120,000 m
Height (h) = 4.5 km = 4,500 m

Volume = π * (120,000)^2 * 4,500 ≈ 2.03 × 10^15 m^3
M = ρ * Volume ≈ 1.3 kg/m^3 * 2.03 × 10^15 m^3 ≈ 2.63 × 10^15 kg

Now, let's calculate the moment of inertia:

I = 0.5 * M * R^2 ≈ 0.5 * 2.63 × 10^15 kg * (120,000 m)^2 ≈ 1.798 × 10^28 kg*m^2

Step 2: Calculate the angular velocity (ω)
To estimate the angular velocity, we can use the assumption that the outer edge of the hurricane has winds exceeding 120 km/h. Let's convert this to m/s:

Speed = 120 km/h = 120,000 m/3,600 s ≈ 33.3 m/s

The angular velocity can be calculated using the formula:

ω = Speed / Radius

ω = 33.3 m/s / 120,000 m ≈ 2.775 × 10^(-4) rad/s

Step 3: Calculate the kinetic energy (KE)
Now that we have the moment of inertia (I) and angular velocity (ω), we can calculate the kinetic energy using the formula:

KE = 0.5 * I * ω^2

KE = 0.5 * (1.798 × 10^28 kg*m^2) * (2.775 × 10^(-4) rad/s)^2 ≈ 7.419 × 10^19 J

Therefore, the estimated energy of such a hurricane is approximately 7.419 × 10^19 Joules.

Step 4: Calculate the angular momentum (L)
To calculate the angular momentum, we can use the formula:

L = I * ω

L = (1.798 × 10^28 kg*m^2) * (2.775 × 10^(-4) rad/s) ≈ 4.987 × 10^23 kg*m^2/s

Therefore, the estimated angular momentum of such a hurricane is approximately 4.987 × 10^23 kg*m^2/s.