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.

To estimate the energy of a hurricane, we will use the formula for the kinetic energy of a rigidly rotating uniform cylinder:

E = (1/2)Iω^2

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

We will first calculate the moment of inertia.

The moment of inertia of a cylinder is given by the formula:

I = (1/2)M(R^2 + h^2)

Where:
M is the mass
R is the radius
h is the height

We can calculate the mass of the cylinder by multiplying the density by the volume:

M = ρV

V = πR^2h

Plugging in the given values:

R = 120 km = 120,000 m
h = 4.5 km = 4,500 m
ρ = 1.3 kg/m^3

V = π(120,000)^2(4,500) = 2.177 x 10^15 m^3

M = (1.3 kg/m^3)(2.177 x 10^15 m^3) = 2.823 x 10^15 kg

Now we can calculate the moment of inertia:

I = (1/2)(2.823 x 10^15 kg)((120,000)^2 + (4,500)^2)

I = 2.26 x 10^25 kg m^2

Next, let's estimate the angular velocity of the hurricane.

The angular velocity can be approximated by dividing the tangential velocity at the outer edge by the radius:

ω = Vt / R

Given that the tangential velocity (Vt) at the edge is approximately equal to the wind speed (120 km/h), and converting it to m/s:

Vt = 120 km/h = (120,000 m) / (3600 s) = 33.33 m/s

ω = (33.33 m/s) / (120,000 m) = 2.78 x 10^-4 rad/s

Finally, we can calculate the energy:

E = (1/2)(2.26 x 10^25 kg m^2)(2.78 x 10^-4 rad/s)^2

E = 1.50 x 10^17 Joules

So, the estimated energy of such a hurricane is approximately 1.50 x 10^17 Joules.

Moving on to the estimation of the angular momentum:

The angular momentum of the hurricane can be calculated using the formula:

L = Iω

Plugging in the values:

L = (2.26 x 10^25 kg m^2)(2.78 x 10^-4 rad/s)

L = 6.3 x 10^20 kg m^2/s

Therefore, the estimated angular momentum of such a hurricane is approximately 6.3 x 10^20 kg m^2/s.

To estimate the energy of the hurricane, we can assume it as a rigidly rotating uniform cylinder of air. The energy of the hurricane can be approximated as the sum of the kinetic energy of the individual air particles within the hurricane.

To calculate the kinetic energy, we can use the formula:

KE = 1/2 * m * v^2

First, let's calculate the mass (m) of the air within the hurricane:

Mass (m) = density * Volume

The volume of a cylinder is given by:

Volume = π * radius^2 * height

Substituting the given values:

Volume = π * (120,000 m)^2 * 4,500 m

Now we can calculate the mass:

Mass (m) = 1.3 kg/m^3 * π * (120,000 m)^2 * 4,500 m

Next, we need to estimate the velocity (v) of the air particles at the outer edge of the hurricane. The question states that the winds can exceed 120 km/h at the outer edge. Let's convert this to m/s:

Velocity (v) = 120 km/h * (1000 m/1 km) * (1h/3600s)

Now we have all the values needed to calculate the kinetic energy:

KE = 1/2 * m * v^2

Finally, we can calculate the energy of the hurricane by plugging in the values we obtained:

KE = 1/2 * (mass) * (velocity)^2

For calculating angular momentum, we consider the hurricane as a rotating body. The angular momentum of the hurricane can be estimated as the product of its moment of inertia (I) and its angular velocity (ω).

The moment of inertia for a uniform cylinder is given by:

I = (1/2) * m * r^2

Substituting the values:

I = (1/2) * (mass) * (radius)^2

Next, we need to estimate the angular velocity (ω) of the hurricane. Angular velocity is the ratio of the tangential velocity (v) at the edge of the hurricane to the radius (r). We can use the velocity (v) value we calculated earlier.

Angular velocity (ω) = v / r

Finally, we can calculate the angular momentum using the formula:

Angular Momentum = I * ω

Substituting the values we obtained:

Angular Momentum = (1/2) * (mass) * (radius)^2 * (v / r)

This will give us a crude estimate of the angular momentum of the hurricane.