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Frisbees normally generate lift because their "wing" is moving through air, so what would happen if I just get the frisbee spinning without pushing its center of mass forward? Assume there is no gravity so there is no falling "parachute effect".

Let's define a frisbee as a 2D cross section which is rotated about the y axis, so that the object has complete rotational symmetry about the y axis. The spin for this experiment is then applied about the y axis and lift is the y component of acceleration. (If there were no rotational symmetry, one could obviously generate lift by using a "helicopter blade", or by simply adding some 45-degree "elevator tabs" to the bottom of a normal frisbee.)

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  • $\begingroup$ By assuming a frisbee as a 2D cross section, do we need to neglect the curvature near the circumference? $\endgroup$
    – Vishnu
    Commented May 9, 2020 at 14:48
  • $\begingroup$ No - That curvature is allowed. As I tried to write in the question, a frisbee is a 3D object with the same 2D cross-section for any rotation angle from which you view it. $\endgroup$
    – bobuhito
    Commented May 9, 2020 at 14:55

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I agree with Rusian. It will produce lift because the skin friction drag of the spinning frisbee will cause the air to move outward from its center as a result of centrifugal force. When the air reaches the lower lip of the frisbee it will be directed downward by the lip, and thereby create lift.

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    $\begingroup$ @Ruslan said there is no lift, so did you mean to write "I disagree with Ruslan"? $\endgroup$
    – bobuhito
    Commented May 19, 2021 at 21:25
  • $\begingroup$ Good explanation. Back-of-the-envelope calculations then tell me that the fastest human throws of the lightest frisbees (if somehow thrown exactly at the same speed as a strong trailing wind, such that there is no relative airspeed) generate lift of about 1% of earth's gravity for about the first second of flight (spin decays quickly for a light frisbee), so we simply don't notice this. Underwater experiments might be an interesting confirmation... $\endgroup$
    – bobuhito
    Commented May 20, 2021 at 19:19
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Imagine a frisbee hanging still (no rotation) in an endless sea of air (no gravity). Obviously, the frisbee will not move. When the frisbee is rotating though, there will develop a rotating motion of air inside the inner confines of the frisbee. This results in a vertex of air moving away from the frisbee (from the non-flat side). As a result, the flat side will move with a steady velocity (air friction). If the frisbee were just a flat cylinder (that is, symmetric), it wouldn't move.

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A frisbee simply spinning with its center of mass at rest will generate no lift. This is easy to see simply by considering that it's not pushing any air downwards. It's the horizontal motion through the air which generates lift. Spin is only needed to stabilize the disc, so that it doesn't wobble or flip over.

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  • $\begingroup$ It could be pushing a little air downwards, how do you know? $\endgroup$
    – bobuhito
    Commented May 9, 2020 at 16:00
  • $\begingroup$ @bobuhito if it pushed a little downwards, it would also push a little upwards, so there'd be no net effect. $\endgroup$
    – Ruslan
    Commented May 9, 2020 at 16:01
  • $\begingroup$ I'd say it's not symmetric (top of frisbee and bottom of frisbee are different), so can't agree so easily. $\endgroup$
    – bobuhito
    Commented May 9, 2020 at 16:05
  • $\begingroup$ @bobuhito if you consider the disc frictionless, then, to the air molecules hitting the disc, it's as good as fully resting: they don't notice that the surface is in motion because there's no force that makes the molecules change direction—other than the normal force, which simply reflects the molecules in a way independent of angular speed. $\endgroup$
    – Ruslan
    Commented May 9, 2020 at 16:10
  • $\begingroup$ Consider the streamlines over a spinning but otherwise stationary frisbee. They are all planar circles. There is no lift-generating component to the flow. $\endgroup$
    – Guy Inchbald
    Commented May 9, 2020 at 16:26
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A real toy frisbee is a little round wing, as long as said wing doesn't exceed its critical angle of attack and air continues to pass over it, it will generate lift!

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Simple. A frisbee without rotation just drops to the ground. But a @Ruskan said, so does a rotating one. It takes rotation for stability and motion relative to the air for a frisbee to generate lift.

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  • $\begingroup$ A frisbee with rotation also just drops to the ground. $\endgroup$
    – Ruslan
    Commented May 9, 2020 at 15:55

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