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So I’m still new to physics so forgive me if it’s a simple question. Assume no air resistance. Suppose I throw a curveball at 30 m/s at an angle of 10$^\circ$ from the horizontal. Assuming I’m not Brad Ziegler (a sidearm pitcher) and I actually threw a good curveball, I think it’s range would be less than that of if I threw a four seam with the same initial speed and launch angle. I.e. the rotation of the ball causes it to fall to the ground sooner than a fastball would. So I have the following questions:

  1. what forces cause the ball to hit the ground faster even though it has the same initial speed and launch angle? This seems to contradict the equations in projectile motion, no?

  2. Would that curveball work in vacuum? Or would it not have enough “air to catch” in its spin therefore not causing it to drop sooner than the fastball would?

Any illuminating guidance or ideas would be very informative for me.

EDIT: I was asked to edit this to ask wbout what the underlying physics concept it. I am confused because my question is precisely what are the underlying physics concepts. This is not a homework question. This is me trying to learn more about physics.

By question can be summarized in the following way: What are the "underlying physics" concepts that cause a curveball to curve? Does it rely on there being an atmosphere? And is it true that a well thrown curveball will have a shorter range (ON EARTH) as a fastball with the same initial speed and launch angle?

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    $\begingroup$ Sometimes when people say, "in space," they mean in vacuum. Sometimes they mean, in free fall. Sometimes they mean both. How about you? (I'm guessing you're not thinking mostly of the radiation environment.) $\endgroup$
    – Solomon Slow
    Commented Dec 2, 2022 at 21:48
  • $\begingroup$ @SolomonSlow Yes you are right should have been more specific: I mean "In a vacuum". $\endgroup$
    – Chris Christopherson
    Commented Dec 3, 2022 at 21:26
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    $\begingroup$ Voting to re-open. I don't know why this was closed as a "homework-like" problem. $\endgroup$
    – Michael Seifert
    Commented Dec 4, 2022 at 14:52
  • $\begingroup$ @MichaelSeifert same. That feature is being abused - this is a 100% genuine physics question $\endgroup$
    – Señor O
    Commented Dec 4, 2022 at 18:25
  • $\begingroup$ @MichaelSeifert I truly appreciate it. $\endgroup$
    – Chris Christopherson
    Commented Dec 4, 2022 at 23:19

2 Answers 2

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I think it’s range would be less than that of if I threw a four seam with the same initial speed and launch angle. I.e. the rotation of the ball causes it to fall to the ground sooner than a fastball would.

Turns out this isn't the case. If there's no air, the balls rotation won't affect its linear velocity. Angular momentum needs to be conserved, and linear momentum needs to be conserved, so without air to transfer angular momentum to linear spinning the ball won't have an effect on its path.

(1) what forces cause the ball to hit the ground faster even though it has the same initial speed and launch angle? This seems to contradict the equations in projectile motion, no?

Again I'll take the conservation of momentum approach: if the spinning ball has more downward momentum than the non spinning ball, it put upward momentum into some other object. What object is that? The air. A curveball only curves downward because it gives net upward momentum to the air around it.

(2) would that curveball work in space? Or would it not have enough “air to catch” in its spin therefore not causing it to drop sooner than the fastball would?

No, it would not curve.

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  • $\begingroup$ In your response to the first question you say "it is not the case" but you seem to mean it is not the case in a vacuum as you immediately say "If there's no air..." But I am wondering if my intuition is correct even on earth: ON EARTH, will a curveball have a shorter ranger than a fastball given the same $|v_0|$ and $\theta$? $\endgroup$
    – Chris Christopherson
    Commented Dec 3, 2022 at 21:28
  • $\begingroup$ @ChrisChristopherson You said "assume no air resistance" - but air resistance is precisely what allows a curveball to curve. "Assume no air resistance" is effectively equivalent to "in a vacuum". $\endgroup$
    – Señor O
    Commented Dec 4, 2022 at 8:01
  • $\begingroup$ @ChrisChristopherson Perhaps what you mean is, if the "air resistance that opposes velocity" was roughly the same between the curveball and fast ball (thus still allowing the curveball to curve), would the curveball still drop faster? Yes it would. $\endgroup$
    – Señor O
    Commented Dec 4, 2022 at 8:02
  • $\begingroup$ Okay understood thank you for the help! I suppose the difference is that when learning about projectiles we assume the constant acceleration vector $\mathbf{a} =\langle 0, 0, -g \rangle$ which is truly constant only if there were really NO air resistance. But on earth, since there is air resistance, the curveball will "use the air around it" to make its acceleration no longer constant? $\endgroup$
    – Chris Christopherson
    Commented Dec 4, 2022 at 23:31
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    $\begingroup$ @ChrisChristopherson yes what you're saying is correct. And it's no coincidence that the amount a curveball curves is roughly on the order of the error you would get from "assuming no air resistance". i.e. if you get 10% error from assuming no air resistance, you'll likely see around 10% difference from the magnus effect on a curve ball vs. non-curve ball. So while in many cases it makes sense to ignore air resistance for projectiles, when calculating how much a ball "curves" you really can't ignore it. $\endgroup$
    – Señor O
    Commented Dec 5, 2022 at 1:35
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The force which causes deflection from projectile motion for a rotating body in a fluid (that is to say, what makes the curveball curve) is the Magnus force. It is a kind of lift, and is a consequence of the interaction of the spinning body and the fluid, much like that caused by angle of attack for a wing. Like other forms of lift, it would not be present in a vacuum.

Addendum edit: the same force points in the upward direction for a fastball (the ball spinning such that the bottom has a larger speed relative to the ground than the top), which would contribute to a longer flight time than a curveball, in which the direction of spin and the resulting magnus force are sideways... other factors being equal. I do not know whether other factors are equal.

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  • $\begingroup$ oh wow! So you say "in a fluid".... but things spinning in "air" is good enough for the magnus force to still apply? Perhaps "In a fluid" has a different meaning in physics than it does coloquially? $\endgroup$
    – Chris Christopherson
    Commented Dec 4, 2022 at 23:25
  • $\begingroup$ @ChrisChristopherson yes, air is a fluid in the physics sense. $\endgroup$
    – g s
    Commented Dec 5, 2022 at 1:13

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