Talk:Rotational energy

Video Example

The article has a video example that currently says:

Paper roll wound up on strings and released to fall, illustrating the rotational energy of a round body and how it strays when in vertical fall because of it. The demonstration is repeated by winding up the roll in the opposite direction, to show that the walling roll will stray in the other direction as a result.

However, the effect shown is Magnus effect from a rotating cylinder generating lift. The rotational energy is not responsible for straying from vertical. A better example would be a heavier cylinder wound on string vs an same weight unwound cylinder. The wound cylinder will fall slower, as its potential energy has to be converted to both rotational and translational energy instead of purely translational. A heavier cylinder will make the aero influence such as the Magnus effect and drag, as well as the contribution to mass from the string, negligible.

I'm going to remove this example. — Preceding unsigned comment added by 73.38.6.198 (talk) 21:46, 12 July 2019 (UTC)

The velocity advantage of Guiana vs Kennedy space centers

The article currently says:

The European spaceport in French Guiana (Guiana Space Centre) is within about 5 degrees of the equator, so space rocket launches (for primarily geo-stationary satellites) from here to the east obtain nearly all of the full rotational speed of the earth at the equator (about 1,000 mph, sort of a "sling-shot benefit). Rocket launches easterly from Kennedy (USA) on the other hand obtain only about 400 mph added benefit, due to the lower relative rotational speed of the earth at that northerly latitude. This saves significant rocket fuel per launch, so this tends to be a relatively more economic spaceport.

However, Kennedy space center is located at 28.6 degrees North (according to Google maps). As the Earth rotates once in 24 hours, the Kennedy space center travels a distance cos(28.6 deg) = 0.878 times the length of the Equator, whereas Guiana travels cos(5 deg) = 0.996 times the length of the Equator. The Equator is 40075 km (24901 miles) long. Divided by 24 hours, I find velocities of 911 and 1034 miles per hour respectively. The number 400 mph for Kennedy space center must be wrong.

In contrast, the Andoya space center in Northern Norway at 69.3 degrees North only moves at 367 mph, closer to the 400 figure.

A rocket sent up from the Kennedy space center, compared to one sent up from the Guiana space center, must make up for the difference in initial speed by burning an extra amount of fuel. If a rocket needs to have a mass $M_{Guiana}$ when sent up from Guiana, it needs to have a mass $M_{Kennedy}$ when sent up from Kennedy, sufficient to reach the initial velocity of Guiana and still having left fuel so that its mass at that point is $M_{Guiana}$. Using the rocket equation, we find that

$M_{Kennedy}=M_{Guiana}e^{\frac {v_{Guiana}-v_{Kennedy}+gt}{u}}=1.023M_{Guiana}$

assuming exhaust velocity $u=$ 3000 m/s relative to the rocket and acceleration 3g. That is roughly a 2.3 percent increase in cost. Cacadril (talk) 12:00, 22 June 2018 (UTC)

Example

Trivial, but the example would flunk any high school physics test. At least, I hope it would. ignoring exponents, the example claims (7.29^2)*8.04 = 2.138. That is, the result has more significant figures than the inputs. Amazing if true, but of course, its not true. Just sloppy applied mathematics. It's been 50 years since I had to worry about this kind of mechanics, but it took me a couple of minutes of research to find that the resulting units rad²kg m²/s² were actually kg m²/s² (which is, of course, Joules) because rad is "dimensionless". That's an even less important point, but some of us learned to keep track of dimensions (units of measure), and I sure didn't remember that radians were dimensionless - and I can't be in the minority on this, since I'm pretty sure my physics knowledge is at least average. I suggest that the result be 2.14 (you could correctly argue that it 'should' be 2.1) and certainly not 2.138. (ignoring exponents). I also think it would be helpful to note that radians (and radians²) are dimensionless. [At least here they are. I'm not certain that's true in all cases? (is 1 radian per meter the same as 1 per meter? IDK).]98.21.219.152 (talk) 19:05, 10 September 2022 (UTC)

Thank you for drawing this to our attention. I can confirm that the radian as a measure of angle is always dimensionless.

Looking closely at the example of launching satellites, and linking that to the Earth’s rotational energy is also flawed. The article is seriously under-sourced so I will take a close look at it later today. Dolphin (t) 23:42, 11 September 2022 (UTC)

I have changed the Earth's rotational kinetic energy from 2.138 units to 2.14 units. See my diff. In examples of this kind, answers should use no more than 3 significant figures. Dolphin (t) 12:32, 12 September 2022 (UTC)