Why do football do not follow a a staring trajectory when kicked with a spin

Question

Can any one explain this ?

Answer 1

It is the job of the scientist, mathematician, etc. to develop explanations of observed physical phenomenon. In Computer Science, I taught students how to model those situations in order to accurately (note: this varies with expertise) predict the outcome.  So, the first principle of action/reaction is taught.  A kicked football travels a straight line forever.

 

But, we observe that this is not quiet true, so we change the equation to include gravity.  Now in Physics, as you indicated, you learn the acceleration (change of speed over time) due to the Earth's gravity that applies.  This gets us past most algebra problems.

 

But, you mentioned not only trajectory, but spin.  Theoretically, with gravity but no air (say, on the Moon), the football would behave differently.  With air (as I learned in Aerodynamics class), we need Calculus to describe the forces at work.  And, with an object like a football (not a sphere), those forces change a lot over time.

 

Not too surprisingly, a properly thrown spiral (of a football) follows the trajectory with its spiral (this is a great calculus problem and even more fun to simulate with animation, in color with sound, on a computer.  Surprisingly, this is not very hard, but schools usually can't afford it or don't understand how to use technology, but you will definitely need it to work as a physicist or engineer or ...

 

Now, in order to explain "wobble," or to explain why soldiers get out of step on a bridge, or why rockets shake violently on ascent, you must study vibrations and harmonic phenomenon.  The math gets harder, the number of people get fewer, the salaries get higher, ... and some are called "rocket scientists."

 

Then, there is the huge consideration of the wind (ask any placekicker).  Trajectories are often based on a coordinate system based on the ground, whereas a football in flight has a moving coordinate system (if you want to use it).

 

Also, the Earth rotates, bugs may crash into the football, under-inflation may introduce extreme shapes to the aerodynamic effects, ... , and rain and cold and rain and ... very, very slightly alter the football's path.

 

Eventually, the model gets refined enough that the sum of all known future factors is negligible.