**1. Frame of reference:**

The golf ball is at the origin of an $x,y,z$ coordinate system (see Fig.1). $x$ and $y$ are in the horizontal plane. The golfer wants to project the ball in the $y$ direction.

**2. Rotational and translational motion:**

The ball is hit in such a way that it acquires an initial speed $v_0$, at an angle $\theta$ (see Fig.2). The ball will now follow a more or less parabolical trajectory (in the absence of air drag it would be perfectly parabolical). This motion is known as *tranlational* motion.

Now the golfer may want to impart on the ball an additional *rotational* motion, known as spin. A rotating object always rotates about an axis, so we can distinguish three possibilities.

a. Rotation around the $x$ axis, which is perpendicular to the axis of translation. Backspin: bottom moving towards the golfer. Topspin: top moving towards the golfer.

b. Rotation around the $z$ axis, in golf known as slice or hook.

c. Rotation around the $y$ axis (axis of translation): not important is sport but this spin is imparted by the rifles of a gun barrel to a bullet and increases stability of the bullet in flight.

**3. Spin in flight:**

Due to the Magnus effect, in air the rotation of the ball causes a drag force acting on it, perpendicularly to both the air flow and to the axis of rotation, because the airflow has been deflected in the direction of spin. Back spin thus causes extra lift and extends the flight path somewhat (see Fig.4).

Similarly, slice or hook causes a horizontal force to act on the ball, creating (left or right pointing) curvature of the trajectory.

**4. Spin on impact:**

Due to conservation of angular (rotational) momentum, spin also has consequences for the ball’s post-impact trajectory. It’s well known that tennis ball with backspin will travel faster and at lower angle (bounce) after hitting the floor, compared to a spin-less ball. This is similar for a golf ball.

A ball with spin/hook will also experience a slight change in horizontal direction on impact with the floor.

**5. Optimal projectile angle:**

A golf ball launched as indicated in Fig.2, in the absence of drag and spin, will reach a horizontal distance (see Fig.3) of:
$d=\frac{{v_0}^2}{g} \sin (2 \theta)$.

It can derived that $d$ is maximum for $\theta=\frac{\pi}{4}$ (45 degrees).

**6. From an energy perspective:**

One could argue that imparting spin on a ball is a form of loading it with extra kinetic energy.

A spinning ball that’s also translating through the air has a translational kinetic energy at the start of the trajectory:

$E_{k,T}=\frac{m{v_0}^2}{2}$, with $m$ the mass of the ball and $v_0$ the initial speed.

But a rotating body also has kinetic energy:

$E_{k,R}=\frac{I \omega ^2}{2}$, with $I$ the inertial moment of the ball and $\omega$ its angular velocity ($\omega = 2 \pi f$ with $f$ the frequency of rotation).

The total initial kinetic energy is $E_k=\frac{m{v_0}^2}{2} + \frac{I \omega ^2}{2}$.

During flight, part of the rotational kinetic energy is converted to work by the Magnus force.

There are two forces that draw the ball into the waterfall (or push the ball upstream), and both of these are much stronger than the two effects mentioned in the question. As a white water kayaker, I have a lot of experience with the relevant forces, and they can both be very strong and sometimes life threatening.

The first force: in broad and uniform flows like this, there is usually an upstream circulation for a significant distance downstream of the drop. To kayakers, this flow pattern is often called "hole", "hydraulic", or "stopper". A cross section looks something like this (my own quick sketch, but there are many better illustrations by searching "whitewater" and the above terms):

As to the forces, even very small drops, like 1 ft, can create extremely powerful upstream flows. I once had a boat stay stuck in such a hole for many hours while defeating every effort to fish it out. These are surprisingly dangerous, partly because they look so innocuous, and it's easy to find discussions of this, (eg, search "low head damn rescue and fatalities"). Or, for a very tense rescue on a bigger drop, see this.

Whether the hydraulic extends to the radius of the ball is difficult to tell from the video.

The other force pushing the ball towards the waterfall is the rotation of the ball which drives it upstream. The falling water will always move faster that the bottom water, and this drives the ball to spin. This spin then pushes the ball upstream against the slower flowing bottom water. That is, in the video the drop is to the left, the ball is to right, and the spin is CCW. The fast CCW spin causes the bottom surface of the ball to be moving faster than the bottom flowing water, and which pushes the ball to the left.

## Best Answer

What produces lift is

circulation, which causes the airflow to be deflected in one direction, causing an equal reaction in the other direction.If you want to think in terms of Bernoulli on your soccer ball, the air on the left side is being slowed, while that on the right side is being accelerated by the spin of the ball.