Is hitting of a shuttlecock a translatory motion ?
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Answer:
Projectile theory is what I can and will explain here. Fluid dynamics aspect is not in my capacity to give as explanation since it involves making one understand Computational Fluid Dynamics, Navier-Stokes Equation, Large Eddy Simulations, Finite Methods, Concept of Vortex exclusively and more. Can you believe to explain shuttle-co
Lets jump to explain plain old projectile.
Shuttlecock always flips on impact, you know that. It flies cork-first. This flipping motion arises from the fact that, unlike almost all other sports projectiles, the shuttlecock has a conical shape and, because the cork is much denser than the feathers, a non-homogeneous mass. I have personally measured and found out a typical shuttlecock has its center of mass about 3.4 cm in front of its pressure-center (the point where all of the pressure forces). The different centers of mass and pressure cause the shuttlecock to exhibit its unique stabilizing aerodynamic torque and its characteristic flip.
In short, if you have a total system of mass that has non-homogeneity along the axis, the trajectory will have a parabolic path. So even if you have a stone tied to bunch of leaves (stiff enough) you will get the same projectile motion.