I'm back. *Free Guy* was quite good. Not quite what I thought it would be. I recommend it (for seeing once).

What follows is my friend's response. Before I get to that… I'd like to thank Bryan Izatt for his post, which does a pretty good job of highlighting some of the things you… didn't get right.

The simplest is is that you said "To put it another way, a reduction of MOI will increase both the ball's spin rate and spin axis." and that's wrong: it doesn't "increase the spin axis." Or tilt it any more, or whatever. The ball just spins: it doesn't differentiate between the X and Y axis.

The rest of the text in this post is his (except the quoted parts, obviously).

A modern high MOI golf ball, in relation to comparable balls from yesterday, does not just have a higher resistance to backspin. The modern ball is more resistant to all rotational forces applied to it.

This is a good start, you recognize that both backspin and sidespin will be proportionately increased.

Conservation of energy illustrates that as the MOI of a golf ball is decreased, the angular momentum would increase.

This is where you start to go wrong - angular momentum is conserved in all cases. An identical strike will result in a golf ball with identical angular momentum at impact, no matter what kind of golf ball you're using. The total impulse imparted onto the golf ball, which equates to the total change in momentum, is the same because the force applied by the golf club and the elasticity of the golf ball are unchanged.

DeltaP (change in momentum, or impulse) = F (applied force) * T (time). The force from the golf club is the same, because the strikes are identical since we are not testing that variable. The duration of impact is the same, because elasticity of the golf ball is not the variable we are testing. The only variable we are changing here is the moment of inertia of the golf ball, and that does not have any effect on the total momentum (angular or linear) imparted upon the golf ball.

L (angular momentum) = I (moment of inertia) * w (angular velocity). Angular momentum is constant, as described above. Moment of inertia is reduced, which means that the angular velocity must be increased resulting in a higher spinrate at impact.

To put it another way, a reduction of MOI will increase both the ball's spin rate and spin axis.

This is where you go off the deep end, reducing the MOI of a golf ball will have no effect on the spin axis because the increase in both backspin and sidespin are proportionate. Let's go back to fundamental physics here to show exactly why:

A sphere with a uniform relationship between density and radius, which a golf ball is, has the same moment of inertia for all possible axis of rotation. This means that the vertical axis of rotation (sidespin) and the horizontal axis of rotation (backspin) have the same moment of inertia. The total angular momentum is equal to the sum of angular momentum along these two axis

L = I * ⍵

L

_{Total} = L

_{Sidespin} + L

_{Backspin} (I

_{Golf Ball} * ⍵

_{Total}) = (I

_{Golf Ball} * ⍵

_{Sidespin})+ (I

_{Golf Ball} * ⍵

_{Backspin})

⍵

_{Total} = ⍵

_{Sidespin} + ⍵

_{Backspin}⍵

_{Sidespin} = Δ L

_{Sidespin} / I

_{Golf Ball} = (F

_{Sidespin} * T ) / I

_{Golf Ball}⍵Backspin = Δ LBackspin / IGolf Ball = (FBackspin * T ) / IGolf Ball

All forces and times are constant - Because we're comparing identical strikes, only changed variable is Moment of Inertia

From here it's easy to see that any change to the golf ball's moment of inertia (IGolf Ball) will have a proportionate effect on both sidespin and backspin. Halving the moment of inertia will double the backspin, and also double the sidespin.

Spin axis = ArcSin( |⍵

_{Sidespin}| / |⍵

_{Backspin}| )

Spin axis = ArcSin{ [ (F

_{Sidespin} * T ) / I

_{Golf Ball}] / [ (F

_{Backspin} * T ) / I

_{Golf Ball}] }

Spin axis = ArcSin{ [ (F

_{Sidespin} * T ) / I

_{Golf Ball}] / [ (F

_{Backspin} * T ) / I

_{Golf Ball}] }

Spin axis = ArcSin{ (F

_{Sidespin} * T ) / (F

_{Backspin} * T ) }

All forces and times are constant - Because we're comparing identical strikes, only changed variable is Moment of Inertia

The spin axis is based off the angular speed of both backspin and sidespin, with (Sidespin/Backspin) equal to the Sine of the spin axis' angle. If you double both the sidespin and the backspin, by halving the moment of inertia, the spin axis will remain unchanged.

As you can clearly see, changing the moment of inertia does not change either the total angular momentum (Force and impact duration are kept constant) nor does it change the spin axis. Literally everything you have written is debunked by the most basic of kinematics taught to freshmen collegiate students and high schoolers around the globe.

For good measure, here are some excellent illustrations from the FlightScope simulator showing exactly how little difference even a monumental increase in spinrate (2500 RPM to 5500 RPM) would have for professional golfers with 180mph ballspeed and a 5 degree spin axis:

Not only are you wrong about what measured values would be different by changing the moment of inertia, you're wrong about what the effects of a monumental difference in spinrate would even look like. You can double the spinrate off the tee and you will barely see any difference in curvature, because magnitude of curvature is primarily dictated by spin axis - not spin rate.