Exploring 2D Motion of Objects: Projectile Motion and Its Variations

[Dirac1238]

I was just wondering is there any major difference between the projectile motion of a 2D object vs the projectile motion of a 1D object or just a point. For example in a 2D world if someone just threw a square, would the calculation of the trajectory be a lot more complicated then calculating a simple regents physics problem involving someone throwing a baseball?

 

[zhermes]

Not at all, its exactly the same if you're ignoring things like air-resistance, etc.

 

[vlado_skopsko]

In every object there is a point ( center of mass ) that is acting as the whole mass of that object is concentrated in it.

 

[Dirac1238]

In every object there is a point ( center of mass ) that is acting as the whole mass of that object is concentrated in it.

yes but what if the 2D square was rotating, would the equation of rotation be different then for let's say a 1D line.

 

[arildno]

yes but what if the 2D square was rotating, would the equation of rotation be different then for let's say a 1D line.

GOOD QUESTION!

As long as we disregard air resistance, then a thrown object will conserve angular momentum, because the only acting force upon the object, gravity, works at the C.M of the object.

Thus, whatever energy associated with the object's rotation initially will be the same during the whole object's flight.

We can, therefore, ignore the object's rotational state when calculating its trajectory.


However, and this is important:
Air resistance is IMMENSELY important in order to describe the actual orbit of, say, a rotating baseball.
This is because the rotation of the ball creates a velocity differential in the ambient air, and therefore, a pressure differential upon itself as well.

This means that in a viscous fluid like air, a rotating ball will get quite a different course than the one predicted for a ball in vaccuum, rotating or not.

 

[vlado_skopsko]

If by equation of rotation you mean angular momentum or angular kinetic energy of the bodies, it is in the field of dynamic, where objects must have mass associated with them and geometry (3d). And from kinematic point of view all the objects are the same because we only look at the center of mass of those objects and arildno explained that very well.