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Moment in Physics

What is “Moment“? In this world of golf in science, it can’t be avoided at all.
Do you really know what does it means?
We had learned these previously “principle of moment” in school .
To understand it easier, “Moment” means the magnitude of force that influences the rotation of an object.
As you can see figure below:

When :(weight ) X (distance from the fulcrum to the action point)= (force) X (distance from the fulcrum).
“Fulcrum is the axis of rotation or point of support on which a lever turns in raising or moving something.”

Please take a look at this equation : ( M = r X F )
-The size of the force “F”
-The distance from the action point to the center of rotation “r”,

-Size of the moment “M”

When a force is used to begin or rotate an object & to stop an object from rotation, a torque is made.
The force applied to a lever, multiplied by the distance from the lever’s fulcrum is described as torque.
To make the answer easier: Both moment & torque are equally same definition.

Is it possible force “F” or the object “r” able to rotate the moment “M” ( F X r =M ) ?
Definitely the answer is : It is impossible.
It causes reverse reaction that influences the rotation/direction of an object.
It appears so frequently in golf ,at this point of view it is easier for everyone to learn the definition “principle of moment” just by making it easier to understand.

Golf Science - Torque

In previous section “moments” on golf science, we knows both  moments and torque are in same definition.
Readers do take note : *
However in golf industry , center gravity of the club head is not on the shaft axis.
During a golf swing, torque causes in various sizes of rotational motion towards toe-side of the shaft.
So how can we measure torque?

By applying the moment that is:1 foot x 1 pound Or in SI unit (ft-lb) it can be evaluates to measure .

A pound-foot is a unit of torque (a vector).
One pound-foot is the torque created by one pound force acting at a
perpendicular distance of one foot from a pivot point.

When converting 1 foot = 30.48cm = 0.3048m 1pound = 453.6g
It will take the moment is 138.26 gm.

As an example :
If this moment over the twisted 5 degrees , “Torque 05 °” term is use to describe in the golf industry.
(As readers can see it from the above picture)
Any curious golfers whom interested on torque measurement it can be done at YUJI GOLF  as well.

Golf Science - Shaft Stiffness by Frequency

In the past few years,we’ve encounter similar comments from most golfers brought their golf clubs
(major golf brands) to us:
“My driver has regular specs shaft but I feel the shaft still too soft for me.”
” When I had good impact , my golf ball goes to the left (hook)”
Does these happens to you as well ?
Each golf shafts indicates stiffness & flexibility which are S , R , AR , L .
In these column on golf science,we explain few methods in golf industries does measurement & difference stiffness of a golf shaft.
1) Measurement in in Deflection Board
Depending on the amount of deflection which is measured by locking the shaft rear at the tip  hanging fixed weights to secure the shaft.

2) Measurement in Frequency

Measure the frequency by  the locking at end of the the shaft’s butt.

3) Measurement In Center Flex

Measuring the shaft strength  by bending the center of the shaft.

In physics definitions of Frequency or r.p.m (revolution per minute) is a unit of frequency of rotation: the number of full rotations completed in one minute around a fixed axis. It is used as a measure of rotational speed of a mechanical component.

The famous calculation in physics that is known as : 1 rpm = 1/min = 1/(60s) = 1/60 Hertz ≈ 0.01667 Hz

What Is Hz (Hertz)? It is part of  our daily life that often seen to name a few such as washing machine,DVD player,audio radio,automoble engines and so on.

Back to the physics again,While Hz (Hertz) is commonlly use by physics, in golf industries by c.p.m (cycle per minute) .

Frequency measurement golf shafts  are in the range of  200c.p.m to 340c.p.m.

Take note  : Shafts by different length with  same frequency  has it’s  difference by  stiffness & flexibility as well.

The best way to know the differences , by comparing two different clubs <S> & < A > shafts.H old the grip up, try to wiggle the club  side to side motion instead of pressing the club down .

Currently, major golf manufacturers knows frequency in shafts are in  golf head speed as well.In fact these has been ignored  & not in demand anymore.Recent mass production & sales in golf industry are likely targeting senior golfers since for the past few years.

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Grips Sizes

About the size of the grip
A) For slicer small size grip is better.

B) For hooker big size grip is better

Is it true?

If you turn the baseball bat by both side, big side easier to turn..It is because one side which the distance from the center is further can put a bigger moment even if power is the same.

Then, big grip is easier to turn. it contradicts B.

Moreover, some people says small size grip is effective to increase the head speed. And big size grip is said that the movement of the wrist is controlled and become better direction control.  Is it true?

The grip size of the putter seems to become bigger every year.

I was surprised when we tested  the special big putter grip of about ten centimeters in diameter ,when working for the manufacturer before .

It was surprisingly easy to get in the hole.

And there is the special practice putter with two shafts in YUJI GOLF. It is also very easy to cup in.

It is very clear to say that for the putter bigger size grip is better.

However, there is a limitation in the size of the grip in the golf rule, and it becomes it as follows 1.75 inches (44.5 mm) if not becoming it even though it measures in any direction. It seems that the golf rule knows big grip is advantageous.

The big butt shaft had become popular before. A thin grip had adhered to the big size shaft end. The size of the rear end of the shaft (It is called butt) is from 18 to about 22mm though 15mm in the diameter is usual.

But it has disappeared from the market in only about two years though it is thought that “The head speed goes up then can get more distance”

It is true that longer club length gives more distance. But club weight must be lighter. If your club length become longer and weight become heavier, you cannot hope that your head speed become faster.

In this respect big butt shaft was advantageous. It was reasonable to make the outside diameter bigger to lighten the shaft and the grip.

About three figures are equal bending strength when thinking at the geometrical moment of inertia, and the sectional area of the big butt (= weight) is halves of a usual shaft.

It is an ultimate lightening to thin the pipe and to enlarge the outside diameter. Though of course (Because it is a carbon shaft), there is a limit.

Coefficient of Restitution

Let’s think about the model of the appearance of the collision of the ball and head before and after the impact by using the coefficient of restitution .
This time let’s think the model of lofted head hit the ball horizontally.
It is an easy example, so-called diagonal collision .
As shown in fig
Head speed before the impact : V
Head speed after the impact : V’
Ball speed : v
Head weight : M
Ball weight : m
Launch angle : θ

The momentum is preserved before and after the collision.
MV = mvcosθ + MV’x …①
We think only about horizontal direction (x direction element) of the coefficient of restitution .
e = - (V’x-vcosθ)/V …②
From ①、②. Ball speed just after the impact is
v = M(1+e)V/((m+M)cosθ)　…③
And Head speed just after the impact is
V’x = (M-em)V/(m+M)…④

There is movement of a perpendicular method (direction of y) because this is an oblique impact, too the ball is upward, and the head moves downward. However, it is possible to move only a little because the head is restrained with the shaft.
To analyze this effect, just replace ①to
0 = mvsinθ - MV’y …①’
Then become
V’y = (mvsinθ)/M …⑤

If you think about not the oblique impact but a simple linear impact, you just take out cosθfrom ①②③.

Well, let’s try to calculate v. (It is easy to do by Excel. )
Ball speed v becomes 58.1m/s
in the case of
V=40m/s, m=45.5g, M=192g, e=0.75, and θ=13deg
and head speed V’x just after the impact becomes 26.6m/s.
You understand that the head has decelerated unexpectedly (40→26.6m/s) though it doesn’t understand too much with the unassisted eye.
It is natural that the head decelerated because the ball speed became 58.1m/s from 0.

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From Yuji Golf

Need to check your equipment & club specs ?

Checking both of your driver and #5 iron on loft , lie ,
face angle ,face progression ,head volume,gravity angle , flex etc

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Measuring your head speed , swing path , face angle ,
impact lie angle ,address posture, H etc

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Using your clubs to analyze your ball speed , launch angle , back spin , side spin, side angle etc

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