It is a simple push or pull. What it ultimately does -- why we are
interested in it -- is cause the object to change its motion. But we
will get to that shortly.

In
order to sharpen the idea what a force is, let's say a bit about what
it is
not.

In the first place, it is not a grab-and-push nor grab-and-pull. As
this
diagram shows, such an action can result in more than just one force.
The forces this hand exerts include:

In red,
the push or pull we have in mind.

A force we have to exert to support the weight of the
object. That is the blue
force the hands apply. It is upwards to prevent the object from going
downward due to gravity.

A pair of forces -- a "torque" or "couple" -- the
hands apply to keep the object oriented vertically. That is the green pair of
forces.

So we have to be careful when we itemize the forces involved in any
analysis, making sure that all the forces are individually accounted
for. We shall see later that they can be combined for the analysis,
but first they must be quantified individually.

Moreover, a force is not a mass. These are often confused.

The diagram shows a pair of one kilogram masses. (You might have called them "weights", but they
are really masses.) In particular:

The one in space is operating without gravity. So it
exerts no force if it just sits there (or really floats there).

The one in a gravity field -- say, on earth -- does
have a force exerted on it. We call that force the "weight" of the
object. Once again, weight is a force, and it is not the same as mass.

OTOH, force and mass have an intimate relationship, which is completely
described in Newton's second law, F=ma.
In a moment, we will go into detail on that.

Yes, I know that there is a gravitational force on masses in space.
It's an unnecessary complication to include in teaching golf, a sport
seldom played in space. So let's not confuse the student here.

Finally,
before we dig into what
forces do, let's mention what a force is mathematically.

A
force is a vector.
The magnitude of the vector is the amount of force.
The direction of the vector is the direction in which the force is
acting.

Since
force is a vector, we can add forces together (but we have to add them
as
vectors) and we can resolve them into components. Both will happen a
lot as we examine how a golf swing works.

Kinetics

Isaac Newton's greatest
contribution to physics is his three laws about forces on
objects. We will first look at the kinetic implications of those three
laws -- that is, how forces between objects (masses) interact to move
the objects. That is the substance of Newton's three laws of motion.

Later we will look at the kinematics -- just the motions themselves. We
do that because it is one of the biggest problems I see when golfers or
golf
instructors or TV commentators
discuss motion. Their confusion of acceleration, velocity, and position
is serious. If you want to understand what is going on, you need a more
proper understanding. Which brings us to Isaac Newton's greatest
contribution to mathematics. Once Newton realized that his
laws demanded a rigorous treatment of position, velocity, and
acceleration, he invented a new kind of mathematics to deal with it:
calculus. We will not be learning calculus here. But we will go through
a bunch of examples of motion and see some patterns. If you can retain
some of those notions, you will be at least partially immunized from
silliness. And if you really understand the examples, you will be very
well positioned to learn calculus if you choose to do so.

Newton's laws

So... Newton had three laws relating forces and motion. Let's take
each in turn and look at what it really means.

Newton's
first law of motion: A
body in motion stays in motion at the same speed and direction (same
velocity) unless acted upon by some force outside the object itself.

This is pretty simple.

If a body is sitting there not moving, it will
continue to sit there and not move. No big surprise.

If a body is moving with some velocity V
(remember, velocity is a vector -- both a speed and a direction), it
will continue to move with that same velocity V
unless a force is applied to the body.

What!?
You mean it won't slow
down over time? That is exactly what it means. If it does slow down,
that means some force was slowing it. There are lots of frictional
forces in the real world, so most things do slow down. But remember,
that was because of a force, a friction force, not because that is just
the way
physics works. In space, where there is almost no friction, things go
on moving for millions and even billions of years.

Let's use Stimp
as a golf example. Newton's first law law says that if you roll a
frictionless ball along a flat, frictionless surface, it should roll
forever. Stimp is a measure of how frictionless the ball and surface
really are. In the diagram, we show the conditions that must attain --
the friction that must be eliminated -- to approach a true "body in
motion" with no force on it.

Stimp
= 5: Kind of a shaggy green. Some fairways probably stimp
here if cut for an elite tournament.

Stimp
= 15:
This is a very fast green, close to the fastest you will see even on
the PGA tour. The grass is trimmed so close, you are almost putting on
packed, dry soil.

Stimp
= 50:
This just plain can't be done on dirt. It has to be a smooth, hard
surface. Concrete or blacktop might conceivably work, but even that may
be too rough; you may need to go to metal plate or something like that.

Stimp
= 150:
Now we've done as much as we can with the surface; we have to look at
the ball itself. To get here, we have to lose the dimples (which are a
source of friction). We may need to make the ball out of steel in order
to (a) get the lossy flex out where the ball's weight slightly
compresses the cover, and (b) increase the mass of the ball so it takes
more frictional force to slow it down. (That's part of Newton's second
law, which we are just a few paragraphs away from.)

Before we go any further, Newton's laws refer to a "body", which I
might also call an "object". It is a real physical thing,
with a mass, a size, a shape -- everything that we think of a
real-world object as having. In real physics, it may be as small as an
atom or as large as a planet. But in golf, we are not going to
encounter objects much smaller than a golf club or human body part, nor
much larger than a person.

Well, I wasn't completely honest
about that. Golf only deals with "Newtonian" physics. But a real
physicist deals with two other kinds of physics that we never encounter
in golf, and probably not anywhere in biomechanics:

"Quantum physics" deals with the world of
tiny particles. When I said "as small as an atom", that would be into
the world of quantum mechanics.

"Relativity" deals with huge
sizes and very high speeds. The sizes can be planets and stars or
larger. The
smallest things where relativity explains behavior are probably black
holes. Relativistic speeds are comparable to the speed of
light. If we think about some twenty-fifth century golf ball going at
500mph, that is still very slow in relativity terms. The error we would
incur by ignoring
relativity would be only 0.00000000005%. (That's ten zeros.)

If someone tells you quantum physics or relativity is important to golf
analysis, they are probably deluded.
So we are studying only
Newtonian physics. Therefore, Newton's laws are a good place to start.

Newton's
second law of motion: If a
force is applied to a body, the body accelerates according to the
relationship F=ma.

The
first law said that things don't change their motion without a force
being applied. This second law says exactly how the motion changes for
a given force. For purposes of discussion, we will apply basic algebra
and F=ma
becomes:

a
=

F m

This way, we see what happens to acceleration when we change force of
mass. So...

Acceleration is defined as the rate of change of velocity.
It isn't how fast something is moving, a mistake that so many people
make. It is how fast we
are changing how fast the thing is moving. Two "how fasts"
in that description, and we'll see why there are two when we get to the
kinematics
of Newton's laws. So far, we are still on the kinetics.

Acceleration
is a vector. It has a magnitude and a direction. The direction is the
same as the direction of the force vector. As for its magnitude...

Acceleration's magnitude is proportional to force (we
know from a=F/m).
Increase the force and you increase the acceleration by the same
percentage as you increased the force. For instance, double the force
gives double the acceleration.

Acceleration's magnitude is inversely proportional to
mass (we know from a=F/m; m is in the
denominator).
Increase the mass and you decrease
the acceleration by the same
percentage as you increased the mass. For instance, double the mass
gives half the acceleration.

For
our example of Newton's second law, we'll do something that involves
numbers -- only fair since the law itself is a formula, F=ma.
Let's figure out what the magnitude is of the force the driver face
applies to the ball during impact. Let's assume that impact produces a
ball speed of 150mph, and that the force is constant during impact.
(The latter is a false assumption, but we'll make it to keep the
calculation simple. At the end of the chapter, we will revisit the
assumption and see how we could have done it more realistically.)

Here's
a diagram of what we need to know in order to solve the problem. (The
photos of the ball and the clubface are frames from an excellent Titleist video.) The
facts:

We know the force
is zero everywhere except during the .0004 seconds the ball and
clubface are in contact. Then it is some number -- and that number is
what we are trying to find.

We know that the acceleration
is proportional to the force because of F=ma.
So the acceleration curve is the same shape as the force curve -- a
line that is zero everywhere except during contact, and a flat top
during contact.

We are given the ball's velocity
is zero before impact and 150mph after separation. We will use
the
international standard for solving this and other numerical problems,
so that is 67 meters per second.

We know that the golf ball has 45 grams
of mass; that's the law! So, if we can find the acceleration, we can
just apply F=ma
to find the force.

Let's get started! The constant force (assumed) requires a constant
acceleration, because mass doesn't change and F=ma.
Now remember the definition of acceleration; it is the rate
of change of velocity. Since the acceleration is constant,
the velocity changes at the same
rate -- the same slope
-- for the duration of contact. That's why the green curve is a sloped
straight line during impact. We need to find the acceleration during
impact; if we can find that, we just apply F=ma
to find the force.

Impact lasts about 0.0004 seconds, a little less than a half
millisecond; we all knew that, right? During impact, the velocity goes
from 0 to
67m/s.

Brief digression. In case you didn't know, "per" means "divided by". For instance you can find miles per hour by dividing miles
traveled by hours spent traveling. That's the way everything in
real-world measurements works. So we write "meters per second" as "m/s", meters divided
by seconds. Now we are going to use that fact.

The rate of change of velocity -- the acceleration
by definition -- is 67m/s per 0.0004 seconds. So we divide 67 by 0.0004
and get a rate of 167,500 meters per second per second (m/s^{2}).
That is the acceleration we were looking for! Note that acceleration is
always units of distance per time squared.

Now we just plug 45 grams (which is .045 Kg for international units)
and 167,500 into F=ma,
and we get:

F = ma
= .045 * 167500 = 7537 Newtons.

Well of course
the international unit of force is named after Newton. What else would
it be?

Let's convert 7537N back into a unit of force we are familiar
with, pounds. That gives us 1694 pounds, or roughly 1700
pounds of force to accelerate the golf ball.

Newton's
third law of motion: For
every force applied by one body to another, there is an equal and
opposite reaction force.

This
final law says that, if you push on something, it will push back with a
force of the same amount and exactly opposite direction. If you pull on
something, it will pull back with a force of the same amount and
exactly opposite direction.

Try it. Push against a wall. Feel it
pushing back? That is real. It is a genuine force, not your
imagination. But if you don't trust your feel, here is a more tangible
demonstration of the third law.

I am sitting in a chair, solidly on the ground. With my foot, I push a
plastic crate full of golf balls (for weight and friction). It slides
along
the ground, following Newton's first law, until the force of friction
stops it. While I am pushing the box with my foot (the red arrow while
I push and acceleration the box), I can feel the box push back at me.
But I don't move, so there is no visible F=ma
on me -- even though I can feel the F.

Then I exchange the kitchen chair for something with a little less
friction. Well, a lot
less friction -- a wheelchair.
Now I do exactly the same thing. This time, the heavy crate has more
friction than my wheelchair, and you can see the reaction force (the
red arrow) at work, performing F=ma
on me.

If these explanations leave you cold, there are lots of other tutorials
on Newton's laws on the Internet. For instance:

NASA has a tutorial page for college, high school, or
middle school students.