I have studied that swept back wings help in delaying the shock waves formed on the wing, but also to my understanding I feel swept back wings reduce the moment of inertia (like for example a ballerina dancer where she spins so easily when she keeps her hands close to her body).
This in turn helps in improving the roll response which is an advantage to a fighter jet. So is my understanding correct?
Yes, for a low-speed aircraft, swept wings are useful to avoid problems with the center of gravity, to move the wing spar into a more convenient location, or to improve the sideways view from the pilot's position. This increases the longitudinal static stability of the aircraft as done by Anglo-Irish engineer John William Dunne.
The slight rearward shift of the aircraft center of gravity is caused by the rearward shift of the wing weight. Indicated by the cross-hatching is the distance between the center of gravity and the center of lift. A small amount of longitudinal stability is highly desirable, but the large increases with sweep angle can cause reductions in aircraft maneuverability and large increases in trim drag. Another issue with variable swept wings is reduced pitch stability due to additional lift and fuse interference. They tend to suffer from lower yaw stability. Also one should note that the mechanism for variable swept wing increases weight of the aircraft.
You also have to keep in mind that variable swept wing aircrafts were designed in an era that focused more on speed rather than maneuverability. The ideology changed after realising the data that showed how much time these aircraft spend in supersonic speeds and hence the focus shifted from speedy to more agile aircrafts.
The Bell Airacobra was designed with the ballerina or ice skater analogy in mind by centering the weight as much as possible. Amazingly, the Dunne swept wing biplane (with rudders at the wing tips too) was rejected as being TOO STABLE for military use!
Sweeping the wing was originally used for issues such as adjusting center of lift. The B17 production design, with its huge new tail and lots of weight aft compared to the prototypes, may have benefited from a little sweep. Adding the chin turret on the G model may have helped with weight balance considerably. Swept wings can be also found in the Tiger Moth biplane.
It was serendipitously discovered that sweep also helps delay the onset of shock waves as one approaches Mach 1 and became very popular at the dawn of the supersonic age. This is a famous story.
Not as often told, but equally true, is making the wings THINNER, as on the Spitfire, also helped a lot.
But as far as ballerinas, it turns out that roll rate is generally improved with shorter wings as on the F16, but weight distribution remains important.
PS Birds do pull the inside wing in while turning, which also helps them slip-turn with their tails.
I feel swept back wings reduce the moment of inertia (like for example a ballerina dancer where she spins so easily when she keeps her hands close to her body).
If you take a straight wing and sweep it back, yes the moment of inertia is lowered.
This in turn helps in improving the roll response which is an advantage to a fighter jet. So is my understanding correct?
No, it is not an advantage to a fighter jet, because planes place aileron control surfaces outboard from the fuselage (closer to the wing tips), as you sweep the wing back, the arm from the aileron to the fuselage gets smaller, resulting in a smaller moment being applied. As a result, your roll response will be smaller if you swept the wing back, despite the lower moment of inertia.
The moment of inertia doesn't get much smaller - fuel tanks are located either in the fuselage or inboard in the wings, so most of the mass stays pretty much where it was before, as the outboard wing sections are empty and light.
The F-14 deployed straight wings during dogfights for better maneuverability, sacrificing top speed.
There is more than just the moment of inertia involved in the roll response, and the response itself is more than just one figure.
Let's consider something like a swing-wing airplane, where nothing changes except for the sweep angle. Furthermore, we'll assume standard ailerons control, which rarely happens on the actual swing-wing aircraft.
The difference in inertia will be noticeable but not that great: most of the mass is still in the fuselage. (Especially this applies to real swing-wings, where it is difficult to carry the fuel and ordinance under the wing). That said, the contribution of the wingtips will reduce as a square of the reduction of the wingspan.
But there are also forces involved. The most significant ones will be the ailerons (control) moment and the roll damping.
If we have ailerons near the wing tips, the moment from them will reduce linearly with the wingspan. At the same time, roll damping depends on the square of wingspan and so will reduce more. Damping reduction is the most drastic effect: the wing is almost exclusively responsible for it. This fundamentally differs airplanes with the proverbial ice-skaters and ballerinas.
Overall, in a typical case, with a longer wingspan you may get faster initial response (ignoring aeroelastic effects, which may reverse the trend even here), but significantly slower sustained roll rate.
Aircraft with short stubby wings may get in trouble due to their fast roll rate, even if (and partly because) their ailerons do not seem that efficient: see inertia coupling.
A wing has three basic design parameters—span, chord and sweep—which are all independent of each other.
Span is always measured along the perpendicular axis of the whole aircraft and chord is always measured along the longitudinal axis. So pivoting the wing around its root will change all three parameters and affect the properties that depend on the,
When designing the aircraft, you choose area (span times chord) to give you the needed amount of lift, then span to give you the desired minimum lift-to-drag speed and sweep for transsonic capability and/or stability. So you should be comparing swept and unswept wing of the same span and area, and those somewhat obviously have the same moment of inertia in roll.
