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# Physics

I love physics, but when you post something as dumb as this, you force me to comment:

Q - If a 6'2" golfer swung at 120 mph, would his ball fly farther than a 5'6" golfer swinging at the same speed? All other things being equal, is this correct?
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A - No, the mass and acceleration in "mass times acceleration" is the mass and acceleration of the club. All things being equal, a 120 mph club swung by anybody is a 120 mph club to the ball regardless of the person hitting it. The velocity of the ball is related to how well the momentum of the club is transferred to the ball. However, in order to accelerate the club, a 6'2" person will use less muscle to get the club up to speed compared to the 5'6" person. That is the mechanical advantage of the moment arm that you mention. Hope this helped.

I responded:

Originally Posted by iacas
That's so bad it's almost entirely misleading.

Not only can people accelerate at different rates and arrive at the ball at the same speed (120 MPH), but it doesn't matter much how tall someone is in regards to acceleration.

Besides, pure kinetic energy or momentum equates are better suited, and they would still ignore things like shaft flex, CoR, where you hit the ball on the clubface, etc. etc. etc. etc.

Finally, a taller person likely has longer arms, too, and since arms weigh more than a club's shaft, the taller person has to accelerate more weight to the same speed. Thus they actually likely do more work than the shorter golfer.

The real advantage taller golfers have is that their swing radius is longer. If they can pivot angularly at the same rate as a shorter person, the clubhead (at the outer end of the radius) moves faster.

I should have said the shorter person actually has to accelerate more quickly... since he has less distance through which to achieve the speed. Though that's only if players swing at the same tempo...

### Re: Physics

There are so many variables in relation to the golf swing. I was walking through the golf section of my local book store and stumbled across a book called The Physics of Golf and just skimmed through it and it looked ridiculous. I'm in Physics right now and whenever we learn new material I think about how it relates to either the golf swing or ball flight, etc.

### Re: Physics

Just hit the friggin' ball for hells sake!

### Re: Physics

Originally Posted by mediaguru
Just hit the friggin' ball for hells sake!

No kidding! Jeez, talk about paralysis by analysis.

### Re: Physics

Originally Posted by NM Golf
No kidding! Jeez, talk about paralysis by analysis.
Uh, some people enjoy thinking about and discussing the physics of the game. After all, where would the game of golf be without an understanding of physics? Not very far. We still might be using dimple-less balls and groove-less clubs.

Just because y'all don't want to participate in a physics discussion doesn't mean ya need to knock it. Some people enjoy it. A few less than that actually make their living off of it.

### Re: Physics

Hi Erik,

This is Matt from GolfTimes.blogspot.com. Thanks for the reply to my post but I'm a little confused as to why you say it's a bad answer and misleading.

First let me say that I didn't ask that question and Chris Murphy,P.E. answered it but I do agree with his answer. Also, I think the question itself was hardly worth asking because as I alluded to in my post , 120 mph is 120mph no matter how you got there, whether you use acceleration or velocity. That is assuming everything else is equal as the person who asked the question stated.

Now, on to your response. Let me respond to the first part (reprinted below):

"Not only can people accelerate at different rates and arrive at the ball at the same speed (120 MPH), but it doesn't matter much how tall someone is in regards to acceleration."

I agree with both parts of this sentence if you assume if everything is equal. It doesn't matter at what rate you accelerate if you arrive at the ball at 120 mph it's 120 mph.

Next part:

"Finally, a taller person likely has longer arms, too, and since arms weigh more than a club's shaft, the taller person has to accelerate more weight to the same speed. Thus they actually likely do more work than the shorter golfer."

I agree that a taller person has longer arms and that they weigh more but I would disagree that he has to work harder to accelerate to 120 mph. You pretty much make my point in your next paragraph:

"The real advantage taller golfers have is that their swing radius is longer. If they can pivot angularly at the same rate as a shorter person, the clubhead (at the outer end of the radius) moves faster. "

A taller golfer naturally creates a longer swing arc and therefore will create a greater centrifugal force than a shorter person which means he would not have to work as hard to get the clubhead to 120 mph than a guy who has a shorter swing arc. Don't foget that everything else is equal according to the original question.

"I should have said the shorter person actually has to accelerate more quickly... since he has less distance through which to achieve the speed. Though that's only if players swing at the same tempo..."

This statement further validates my statement that the shorter guy has to work harder to accelerate his club to achieve the same impact speed as the taller golfer.

Did this make any sense or are we still standing on the opposite sides of the fence?

### Re: Physics

Originally Posted by Mattb
I agree with both parts of this sentence if you assume if everything is equal. It doesn't matter at what rate you accelerate if you arrive at the ball at 120 mph it's 120 mph.

Acceleration doesn't stop at the ball and since the ball is in contact with the club face for a few thousandths of a second, the rate at which the club was accelerating prior to impact plays a role in how far the ball will go. Which would be a nod in the direction of the shorter player, since he would have had to accelerate at a faster rate to reach 120 by impact. However, the longer swing radius of the taller player allows the ball to remain on the club face a little longer, basically nulling this point of the argument.

Originally Posted by Mattb
"Besides, pure kinetic energy or momentum equates are better suited, and they would still ignore things like shaft flex, CoR, where you hit the ball on the clubface, etc. etc. etc. etc."

CoR and shaft flex shouldn't enter into this discussion because the person who asked the question says that everything else besides the person's height was equal so we have to assume these variables were the same.

Touché

Originally Posted by Mattb
"Finally, a taller person likely has longer arms, too, and since arms weigh more than a club's shaft, the taller person has to accelerate more weight to the same speed. Thus they actually likely do more work than the shorter golfer."

I agree that a taller person has longer arms and that they weigh more but I would disagree that he has to work harder to accelerate to 120 mph. You pretty much make my point in your next paragraph:

"The real advantage taller golfers have is that their swing radius is longer. If they can pivot angularly at the same rate as a shorter person, the clubhead (at the outer end of the radius) moves faster. "

A taller golfer naturally creates a longer swing arc and therefore will create a greater centrifugal force than a shorter person which means he would not have to work as hard to get the clubhead to 120 mph than a guy who has a shorter swing arc. Don't foget that everything else is equal according to the original question.

There is no such thing as centrifugal force. That "phenomenon" is just Newton's First Law (An object in motion tends to stay in motion...) in relation to radial motion.

The actual force you're referring to is Centripetal Force or the force directed inward from the apex of the arc (from the clubhead to the grips in this case). I know, it seems to make absolutely no sense, but its true.

### Re: Physics

Hey Jeff, good job on the explanation. I don't know if your right or not but I'll assume you are because it sounded good. BTW, Erik made a reply on my blog (www.golftimees.blogspot.com) and I responded to him which I'm not sure made total sense but you can see it for yourself if you like.

Erik, let me know what you think.

### Re: Physics

Originally Posted by Mattb
Hey Jeff, good job on the explanation. I don't know if your right or not but I'll assume you are because it sounded good. BTW, Erik made a reply on my blog (www.golftimees.blogspot.com) and I responded to him which I'm not sure made total sense but you can see it for yourself if you like.

Erik, let me know what you think.
I think that without an understanding of physics, it's tough for you to debate this topic, just as I think it was irresponsible (though very mildly so) to post it to begin with.

Newton, a great physicist, said three things regarding all motion...

One - A body at rest stays at rest and a body in motion stays in motion,

with uniform velocity, unless acted upon by an outside force.

Two - The acceleration of a body is directly proportional to the force applied

to it and inversely proportional to its mass.  This just means more force yields

greater acceleration and vice versa.

Three - If a force is applied to a body, the body simultaneously exerts a force

of equal magnitude and in opposite direction to that which applied the force.

Swing speed and momentum, believe it or not, have nothing to do with how far the ball will go.

What makes the ball accelerate off the tee is force applied to the club.

Greater force means greater acceleration.

Suppose one man hits the ball twice as fast as another, yet both with

equal force; both balls will travel the same distance, all other things being equal

(all other things are not equal if there is variation in the direction the force is applied

to the ball).

This seems to indicate that shortening the back swing and applying more force to the club

shortly after the downswing begins, makes it easier to hit the ball in the right direction.

But I wonder, is it uniform force (uniform acceleration) that one seeks or is it

a gradual increase in force (acceleration of acceleration)?

In any event, I think it's very clear de-accelerating in the downswing results in pitiful shots.

When I read Erik's (7 year old !!!!) OP the first thing that popped into my head was that this silly question is just the "what weighs more, A pound of rocks or a pound of feathers?" Trick question twisted into a golfing scenario. :)

Got to love collisions, acceleration means nothing in impacts, all it dictates is possibility for higher or slower velocity, which governs the physics on this point.

Is there a correlation between height and golf ball distance, yes, but its because they just have an advantage in being able to generate speed with less effort (body rotation)

Quote:
Originally Posted by Michael Lee

Newton, a great physicist, said three things regarding all motion...

One - A body at rest stays at rest and a body in motion stays in motion,
with uniform velocity, unless acted upon by an outside force.

Two - The acceleration of a body is directly proportional to the force applied
to it and inversely proportional to its mass.  This just means more force yields
greater acceleration and vice versa.

Three - If a force is applied to a body, the body simultaneously exerts a force
of equal magnitude and in opposite direction to that which applied the force.

Swing speed and momentum, believe it or not, have nothing to do with how far the ball will go.
What makes the ball accelerate off the tee is force applied to the club.
Greater force means greater acceleration.

Suppose one man hits the ball twice as fast as another, yet both with
equal force; both balls will travel the same distance, all other things being equal
(all other things are not equal if there is variation in the direction the force is applied
to the ball).

This seems to indicate that shortening the back swing and applying more force to the club
shortly after the downswing begins, makes it easier to hit the ball in the right direction.
But I wonder, is it uniform force (uniform acceleration) that one seeks or is it
a gradual increase in force (acceleration of acceleration)?

In any event, I think it's very clear de-accelerating in the downswing results in pitiful shots.

You're misapplying F=ma here. You'd be better served using impulse-momentum dynamics (another result of Newton's genius).

Agree, your miss-using the F=ma

The reason is, when they figured out Momentum, it includes force. What happens is, in the derivation for the momentum equations, its simplified to mass x velocity

So it does incorporate F = ma, but acceleration isn't used in its final form. This proves in the collision between a clubhead and golf ball its velocity that matters, not acceleration. You will find in physics that acceleration isn't used much. The reason is, that a lot of equations are simplified and combined into simple terms.

This is why a bullet does damage to the body, not through mass, but by velocity. When a bullet hits you, its doing 0.5*M*V^2 energy on the other body. So when a bullet hits you, its not accelerating, in actually its deaccelerating, because the initial velocity is less than the final velocity when it hits you. So acceleration is negative. So, as you can see, in impacts, its velocity not acceleration, if so then guns would do shit damage :p

Quote:
Originally Posted by saevel25

Agree, your miss-using the F=ma

The reason is, when they figured out Momentum, it includes force. What happens is, in the derivation for the momentum equations, its simplified to mass x velocity

So it does incorporate F = ma, but acceleration isn't used in its final form. This proves in the collision between a clubhead and golf ball its velocity that matters, not acceleration. You will find in physics that acceleration isn't used much. The reason is, that a lot of equations are simplified and combined into simple terms.

This is why a bullet does damage to the body, not through mass, but by velocity. When a bullet hits you, its doing 0.5*M*V^2 energy on the other body. So when a bullet hits you, its not accelerating, in actually its deaccelerating, because the initial velocity is less than the final velocity when it hits you. So acceleration is negative. So, as you can see, in impacts, its velocity not acceleration, if so then guns would do shit damage :p

I am not misusing Newton's second law that says F = ma

While it's true momentum is a product of mass and velocity and is conserved over collisions.  It is also equal to the magnitude of force applied to a body and the duration of time it's applied.  Since you can't do anything to about the time applied, the only thing that matters is force.  Force is directly proportional to acceleration and causes acceleration in other bodies and not the other way around.

A bullet causes damage, not by its velocity, but because the human body applies a force on the bullet to stop it - see Newton's first law.  Since the area of the resulting opposite force is so small, it causes tremendous damage; that is why law enforcement officers wear kevlar vests, as it spreads the energy out over a greater surface area.

If you believe momentum or swing speed is desirable, and not acceleration of the club head, think of this...  suppose there are two golf balls suspended in front of a large moving train  traveling with uniform velocity and a small sports car accelerating quickly; both strike the ball at the same speed.  The momentum of the train is huge, yet the momentum of the car is small in comparison; The car will knock the ball much further than the train.

Else, just de-accelerate slightly on the down swing and tell me about the shot.

Please don't stick your tongue out me - it's unnecessary.

Quote:
Originally Posted by Michael Lee

While it's true momentum is a product of mass and velocity and is conserved over collisions.  It is also equal to the magnitude of force applied to a body and the duration of time it's applied.

Yes, and that's impact/momentum dynamics. ∆P = m∆V = F∆t.
Quote:
Originally Posted by Michael Lee

Force is directly proportional to acceleration and causes acceleration in other bodies and not the other way around.

I believe this is what's tripping you up.

The force applied to the ball from the club (and vice versa) has nothing to do with the acceleration of club as it's approaching to the ball. It has much more to do with the accelerations of the ball and club as they leave impact.

Let's say that impact is t=0, so anything pre-impact is negative t. Acceleration of the club at t=-1 doesn't matter. Acceleration of the club and of the ball at t=1 (more like t=.0000001) does,.

Again, I'm not sure why you're so eager to shoehorn F = ma into this when it's much easier to go without it.
Quote:
Originally Posted by Michael Lee

If you believe momentum or swing speed is desirable, and not acceleration of the club head, think of this...  suppose there are two golf balls suspended in front of a large moving train  traveling with uniform velocity and a small sports car accelerating quickly; both strike the ball at the same speed.  The momentum of the train is huge, yet the momentum of the car is small in comparison; The car will knock the ball much further than the train.

You haven't proved that in the slightest, because it's not true. Do the math out, or just look at golf swing data.

Or, logic it out: If my car runs into a golf ball, do you think the golf ball "knows" or "cares" about how fast my car was going a second ago? Two seconds ago? Yesterday? Sure, theoretically the car's speed after impact matters in a problem where the masses are relatively similar, but in this sense, where any deceleration of the car or the train can be treated as negligible, do you really think it "matters" to the golf ball how fast my car is going? It doesn't.

Here's another little point than may be a bit off-topic: If you're striking the ball (let's assume with a driver), and the clubhead is still accelerating (at t=-.0000000001, to use my earlier example), you're leaving power on the table. You're saying, "well, I could hit the ball at 105 MPH, but I'd rather do it at 100 MPH." Sorry, that's going to cost you distance. They've done this testing with professional golfers; search for it on here, Erik (iacas) has posted about it.

I'll quote him below:
Quote:
Originally Posted by iacas

Accelerating what through impact?

The thing that people believe should accelerate through impact is the clubhead, and even that should reach maximum speed at the ball. If it's still not reached maximum speed until after the golf ball, you've wasted speed with bad timing.

Everything slows down incrementally, and everything is decelerating after impact (or should be).

P.S. It's quite literally impossible for a human being to accelerate the clubhead during impact with a golf ball. Unless, perhaps, the golf ball is barely touched.
Quote:
Originally Posted by iacas

A week or two ago, a golf instructor posted this question to fellow instructors on Facebook.

Two golfers, one male, one female, have identical numbers on a launch monitor - launch angle, spin, clubhead speed, etc. Why does the male hit the ball 30 yards farther?

Several people wrote to say what's correct - that if their numbers (all of their numbers for their impact conditions, including smash factor and ball speed) were identical, the balls would fly identical distances, and that's that. Something was wrong.

We later learned that the numbers were given to us from a range session, but the distances were from play on the course. Clearly the guy must swing harder or otherwise change his launch conditions on the golf course.

The thread was revealing, however. Science has taught us that the only thing that matters during impact is the clubhead and about 3-5 inches of the shaft. The collision between the ball and the clubhead are almost like two free bodies hitting each other. Nothing above the 3-5 inches up the shaft has any influence on impact.

Yet pros were chiming in to say "the male probably weighs more, and F=ma" or "the guy probably has a firmer grip" or some other things I've since forgotten.

Rubbish. We know this to be rubbish, or else Iron Byron wouldn't be able to keep a ball on the range. The simple (slightly over-simplified) reason: impact lasts so short an amount of time that the vibrations and deformations and whatnot that occur to the shaft don't have time to radiate up and back down the shaft very far. That's why only the bottom section of the shaft matters. It doesn't matter if you're squeezing the grip so hard you're cracking your shaft or if you literally let go of the grip at the precise moment of impact - the ball will go the same if the launch conditions are the same.

One of the more common - and frustrating - examples of "bad science" is F=ma. This formula - force = mass * acceleration - is used all the time to explain clubhead and ball interaction. But there are a few problems with this:
1. EVERY clubhead decelerates when it hits the golf ball. It can't help but do so with any kind of golf shaft. Really simple physics there.
2. If we consider the exact instant when impact starts, a clubhead traveling 100 MPH will hit a ball a certain distance. A clubhead accelerating will hit the ball within about an inch of a clubhead decelerating into impact.

Consider this: would you rather be hit by a car going 1 MPH but accelerating or the same car going 100 MPH but slamming on the brakes?

If you want to talk about clubhead/ball collision physics, you're better served (though not fully, of course, as neither the golf ball nor the clubhead are rigid bodies) using E=1/2mv^2. You'll note that only the mass (clubhead, bottom 3-5 inches of the shaft) and the velocity of the clubhead matters - there's no consideration for acceleration.

F=ma does apply to the golf swing, however, but the way it's often used is backwards. It would be more appropriate to see how a clubhead is accelerating and deduce the force required to make it do so. Of course, the problem with that is that F=ma is more of a linear concept, while most of the golf swing involves rotation (where an object that has the same linear speed is always "accelerating" because "acceleration" is a change in the velocity of an object - and velocity is both speed and direction).

Another? Conservation of angular momentum. The classic example is that a skater goes into a spin. They pull their arms in tight and they spin faster, they put their arms out and they slow down.

COAM is used in the golf swing to describe why the hips slow down and the torso speeds up, then the torso slows down and the hands speed up, then the hands slow down and the clubhead speeds up.

The problem with using COAM is that it too is inaccurate. COAM applies quite nicely to closed systems (given the relatively low amount of friction on ice and due to the air, a skater is a reasonable example of this). The human body is not a closed system - we can use muscles to slow and speed things up.

And the most damning thing may be the very definition of the word "conservation." In science, "conservation" means "to keep the same." What is a golfer's angular momentum at the top of his backswing? Roughly 0. So if we conserved that angular momentum, the golfer would never make a downswing (or the parts swinging down would have to be offset by the parts swinging the other way - THAT's a swing I'd like to see!).

We can make a downswing because our muscles - which are "inside" the system (our bodies) - can continually add forces, change (increase) angular momentum, etc.

The point? There's a lot of junk science out there. Don't fall prey to it.
Quote:
Originally Posted by Michael Lee

While it's true momentum is a product of mass and velocity and is conserved over collisions.  It is also equal to the magnitude of force applied to a body and the duration of time it's applied.  Since you can't do anything to about the time applied, the only thing that matters is force.  Force is directly proportional to acceleration and causes acceleration in other bodies and not the other way around.

F=ma is best applied to determine how much force our muscles need to exert to cause the clubhead to arrive at the ball at a high rate of speed.

How much farther does a golf ball travel when hit with the exact same impact conditions, but one clubhead is accelerating and another is decelerating. I'll spare you the thought: you won't be able to tell the difference in any real world tests, even on the calmest of days.

Quote:
Originally Posted by Michael Lee

A bullet causes damage, not by its velocity, but because the human body applies a force on the bullet to stop it - see Newton's first law.  Since the area of the resulting opposite force is so small, it causes tremendous damage; that is why law enforcement officers wear kevlar vests, as it spreads the energy out over a greater surface area.

You like to look at things backwards, don't you? The body isn't applying the force. The bullet is the one with the velocity. It applies force to the flesh/bone/etc., the body reacts.

Quote:
Originally Posted by Michael Lee

If you believe momentum or swing speed is desirable, and not acceleration of the club head, think of this...  suppose there are two golf balls suspended in front of a large moving train  traveling with uniform velocity and a small sports car accelerating quickly; both strike the ball at the same speed.  The momentum of the train is huge, yet the momentum of the car is small in comparison; The car will knock the ball much further than the train.

No it won't. The impact interval is far too short for any acceleration to matter.

Here's a question for you: If you were to stick your hand out and smack a solid metal plate as it whizzed by you, would you rather that plate be attached to a high-speed train traveling at 300 MPH, or a sports car that can hit 60 MPH in 2.3 seconds (26 MPH/sec) 20 feet from where it starts off at a stop?

If you like your hand, you'll take the sports car every time.

Quote:
Yes, and that's impact/momentum dynamics. ∆P = m∆V = F∆t.

Here's the thing

m*(v1-v2) = m*a*(t1-t2)

So you get Change in velocity = Acceleration * change in time, basic definition of velocity and acceleration.

So while you want to include acceleration, your basically already did because velocity accounts for it. The thing your doing is transforming velocity into acceleration by its basic definition. So acceleration doesn't add anything to the situation. The reason is your adding in time, so it all equals out. The math there proves it, your saying.

m*deltaV = m*a*deltaT

So there EQUAL. Meaning acceleration can't add anything more to the system because its equal to the other side. You can't just throw acceleration in. Because there is no other term there. There equal.

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