How Much Energy is Stored in a Hurricane's Rotation?

[sinclair18]

Rotational Motion Question -- please help

Homework Statement

Estimate the energy stored in the rotational motion of a hurricane. Model the hurricane as a uniform cylinder 300 km and 5 km high, made of air whose mass is 1.3 kg/m^3. Estimate the outer edge of the hurricane to move at a speed of 200 km/h.

Homework Equations

KE = (1/2)*I*w^2

v= wR

For a uniform cylinder, I=(1/2)MR^2 (but it's hollow so would that make a difference, even though you're only given one radius)

The Attempt at a Solution

So here's how I started out:

KE = (1/2)*I*w^2

v= wR

--> Therefore KE = (1/2)[(1/2)MR^2][v/R]^2

The answer is 4E17 J, but I can't seem to get that. Can someone please tell me where I'm going wrong? I've been doing this problem for so long and I'm just not getting what I keep doing wrong. I feel like it might have something to do with the mass I'm using (M=1.3 kg/m^3) or the fact that I'm neglecting the height (h=5km)? It's not supposed to be a difficult problem...please help!

 

[Curious3141]

Homework Statement

Estimate the energy stored in the rotational motion of a hurricane. Model the hurricane as a uniform cylinder 300 km and 5 km high, made of air whose mass is 1.3 kg/m^3. Estimate the outer edge of the hurricane to move at a speed of 200 km/h.

Homework Equations

KE = (1/2)*I*w^2

v= wR

For a uniform cylinder, I=(1/2)MR^2 (but it's hollow so would that make a difference, even though you're only given one radius)

The Attempt at a Solution

So here's how I started out:

KE = (1/2)*I*w^2

v= wR

--> Therefore KE = (1/2)[(1/2)MR^2][v/R]^2

The answer is 4E17 J, but I can't seem to get that. Can someone please tell me where I'm going wrong? I've been doing this problem for so long and I'm just not getting what I keep doing wrong. I feel like it might have something to do with the mass I'm using (M=1.3 kg/m^3) or the fact that I'm neglecting the height (h=5km)? It's not supposed to be a difficult problem...please help!

What you're given is not a "mass" of air - it's the density of air. Units are mass per unit volume.

What's the volume of a cylinder? Hence, what is its mass? Work in symbols throughout (try to use LaTex, if possible), as there's less chance of error.

You definitely need the height that's given. Also, I'm assuming that 300km is the diameter, not the radius?

 

[sinclair18]

Yeah I just figured it out actually thanks soooo much!

 

[Curious3141]

Yeah I just figured it out actually thanks soooo much!

No problem. Glad to help (if I did).