# Putt Physics Calculation 01: Swinging motion of putt

Are you a golf beginner struggling with your putts? Fear not, as I’ve got you covered with some classic tips that you’ve probably heard before.

First things first, make sure to position the ball directly under your eyes. This is crucial because if your eye level isn’t aligned with the ball, you won’t be able to putt accurately.

Additionally, it’s important to synchronize your backswing and follow-through. This helps maintain a consistent rhythm, which is essential for hitting accurate putts. You should also pay attention to your grip. Avoid using your wrists as much as possible, as this will hinder your accuracy.

Finally, it’s crucial to swing as straight as possible. This will ensure that the ball travels towards your target, rather than veering off-course.

But let’s be honest, all these tips may make you feel like you’re being instructed to become a pendulum. If that’s the case, I highly recommend the app “Putt Physics.” This app calculates your putting swing as a pendulum motion, which means even beginners can hit accurate putts.

If you learned about physics in school, you may have heard of a pendulum motion. The basic components of a pendulum are a string and a weight attached to the end of the string. Although it’s a simple structure, understanding the mechanics of a pendulum motion may help you hit more accurate putts.

Here’s what it looks like:

For instance, if we designate the length of the string as “L,” the weight of the ball as “m,” and the acceleration of gravity as “g,” we can derive a formula based on the conservation of mechanical energy:

$$mgL(1-cos\theta)=\frac{1}{2}mv^2$$

At the highest point of the ball’s trajectory, its potential energy equals its kinetic energy at the lowest point.

When it comes to putting, it’s important to consider the length of the string, which is equivalent to the length of a pendulum swing. Unlike a simple pendulum, however, there are some key differences to consider. First of all, we have to determine the length of the string, which is typically determined by one’s height. However, according to “Putt Physics,” subtracting 30 centimeters from your height is the way to go.

At the end of the string, we have the putter head. The problem lies in determining the pivot point. I was advised not to move my head during the putt, so I chose the center of my shoulders as the pivot point. However, the position of the pivot point can vary from person to person, so it’s important to find the right one for yourself.

By the way, “Putt Physics” suggests subtracting 30 centimeters from your height to determine the length of the string, but keep in mind that this is just a rough estimate. You also have to consider how your body position changes when you putt, so it’s important to experiment with different string lengths based on your individual form and style.

Let me break down some of the physics behind the swinging motion of a golf putter, but let’s keep it light and humorous! So, we’ve talked about the length of the string L in our last explanation, but now let’s discuss the mass of the weight, m. Because it appears on both sides of the equation, we can easily eliminate it by dividing it. Yes, you heard it right – the weight of the weight of the putter has absolutely no effect on the swinging motion of the pendulum. In other words, no matter what putter you use, the ball’s movement will remain the same.

But, of course, that’s a lie. In reality, it’s not the case. While the mass of the weight m does not have an impact on the simple pendulum equation, it does have an impact on the collision between the putter and the ball, as we’ll explain later on.

Additionally, the angle θ represents the highest point of the pendulum’s swing and corresponds to the angle at which the putter is swung during a stroke. The velocity v represents the speed of the weight, which means it corresponds to the speed at which the putter head moves.

Now that we have substituted all the elements, we can perform calculations since we know the numbers, and solve the equations of motion.

Once we know the velocity v at which the putter head is moving when it reaches the lowest point, we can perform calculations since the energy is transferred from the putter to the ball at the time of collision, making the next movement of the ball possible.

In other words, the swinging motion of a golf putter is affected to a greater extent by factors such as the club’s characteristics, the angle of the swing, and the velocity, rather than the weight of the putter or the mass of the weight.

$$v=\sqrt{2gl(1-cos\theta)}$$

Let’s do some calculations! Suppose a person who is 170cm tall swings their putter at an angle of 30 degrees. The length of the string is 140cm because 170cm – 30cm = 140cm, so we can perform the following calculation.
$$v=\sqrt{2\times9.8\times140/100\times(1-cos30^\circ)}=0.606321938$$

That’s it for calculating the putter head speed. In fact, this calculation is performed in “Putt Physics.”

Moving on to swing advice, have you ever been told that “keeping the same rhythm is important” during a putt? Believe it or not, this advice is related to the physical law of a pendulum motion.

When the length of the string and the mass of the weight are the same, the law states that “the motion cycle does not change even if the highest point is different.” When you create a pendulum and set it in motion, you can observe this law in action, and it’s quite fascinating.

On the other hand, if you change the rhythm of your swing in response to the swing arc, then you’re applying a different physical law from pendulum motion. For instance, if you’re performing a swing that slows down when you have a large backswing, compared to the pendulum motion, your putter head speed will slow down. As a result, if your swing arc causes a rhythm change, you must be cautious since it won’t match the swing arc calculation from “Putt Physics.”

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