Pi (π) and Spinning Tops = a Natural Match

by Kevr102 in Workshop > Science

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Pi (π) and Spinning Tops = a Natural Match

Pi (π) and Spinning Tops = a Natural Match
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Spinning Tops are basically classed as toys but there is an actual science behind the Humble Spinning Top and this is where Pi comes into it's own.

Pi (π) is fundamental to circles and rotation, and spinning tops are all about angular momentum and rotational symmetry.

Long-Spinning Tops = Smart Designs + Good Materials.

We could use manual inertia (flick or twist with fingers) or a powered spinner is practical and allows flexibility and greater spin times.

Incorporating ball bearings is a game changer for reducing friction—especially if you use a ceramic or steel bearing at the tip for smooth, long spins.

After downloading various 3D printed spinning top designs many claiming to have long spin times I found out this was not the case and the majority would barely attain a 1 Minute spin time.

When I first started this project I myself thought that spinning a top for a good length of time would have been relatively easy, how wrong could I have been, with my own initial 3D printed designs I struggled to reach a minute with a manual finger spin, I thought at that time that this project needs a science boost in the form of physics to kick start it.

At the culmination of this project I had a recorded manual spin time of 3.5 mins and a non recorded spin time of 10 minutes with a powered spin, but a recorded powered spin time of 8 + minutes.

To create these creations we will be using Fusion 360 and a 3D Printer, we will design spinning tops which use either steel/Ceramic balls, I have 6.3mm and 5mm Ceramic Balls to hand.

We have the concept, next up is the supplies we need then the design concepts.

Supplies

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3D Printer

PLA Filament

6.3mm Steel Balls (Amazon)

5mm Ceramic balls(Amazon)

Epoxy glue or CA Glue(Amazon)

6mm x 6mm Momentary switch.(Amazon

12v DC Motor 385 Micro Motor( Amazon)Motor Body Size: 27.5 x 38mm (D*H); Total Length(including shaft and pin): 60mm; Shaft Diameter: 2.3mm.

Dupont cables or similar.(Amazon) 22AWG cable red and black would be suitable.

2 DC Motor screws, these are approx 2mm x 8mm

9v Rechargeable batteries, which is what I used but standard 9v batteries will be fine.


Design Concept: Pi-Precision Spinning Tops

Key Design Features:

Precision Geometry with Fusion 360

Using Fusion 360, each top is meticulously modeled with precise circular profiles and balanced dimensions. The designs are fine-tuned to ensure symmetry, which is critical for stable, long-lasting spins.

Optimized Mass Distribution

Tops are printed with solid bases for stability and inner voids near the center to reduce central weight, concentrating mass at the perimeter. This increases rotational inertia—a concept directly tied to Pi through the formula for moment of inertia in circular objects (I = ½ m r²).

Threaded Spindles for Modularity

The tops feature threaded spindles, allowing for easy swapping of different tip designs and materials (e.g., metal, ceramic bearings). This modularity supports experimentation and performance tuning.




Fusion 360 Top Design Process

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I wont go through the process of creating new components and sketches within Fusion 360, there are many great tutorials online which can explain the process much better than I can.

I can show the design process I use to design these spinning tops in this Instructable.

The way I opted to go was to create sketches on the front plane, and from this create a center line for our axis.

We need a point for the top to rotate on whether it will be 3D printed or ball, the thing to remember after various designs was to keep the center of gravity low creating less drag from beneath the top.

You will see in the first sketch how we created the inner void in the top, the fillets were applied at the sketch stage but could easily be applied as a solid, there needs to be a solid center so we can thread it, and make it easy to change spindle and top designs, we need to think about how the model will print as well, in this case the top will print inverted.

Using the revolve tool gives us the solid body we need and we can now add a 8mm center circle for the thread, the depth will be 6mm, and best case with 3D printed threads is to apply off-sets to the threads on both Male and Female components, FDM printing has to use a seam somewhere, there are 4 options in the slicer and none are any good for threads.

Using Fusion 360 is great for these type of projects where we can easily create sketches and turn them into solids, fillets can be added and we can create an off-set face at the pointed end of the sketch and use the sphere tool to create the ball size we need and in turn use this to create the void needed for the steel or ceramic ball to sit in.

My initial tops were approx 50mm in diameter with a depth of 12mm these values increased in later tops to create more outer edge mass.

Another useful factor at the design stage was to have the screw in spindle for both manual and powered spins, this was for ease of swapping to different designs, this worked very well at the testing stage.

Please check out the various screen shots which show the sketch process and the section analysis showing clearly the voids which were designed into the sketch.

Motorized Spin Launcher

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To consistently test and push spin performance, I designed a high-RPM DC motor-powered launcher, this can only be described as “an electric screwdriver on steroids.” It applies a one-way clockwise spin via a self designed crank-style release system, similar to starting an old car with the start handle, this ensures peak rotational speed with little or no friction at the release stage.

The 12v DC Motor used for the launcher is 10000 rpm which used with a 9v battery should give us enough energy to spin our tops, too many revolutions will be hard to control.

The one way crank and release system is designed to not only to crank and release quickly and efficiently but also to hold the top in a vertical position as well prior to the release making it a one handed operation if desired, I prefer to steady the top with my left hand prior to launching.

The design of this powered spinner was sketched in the same way as the tops, starting with a vertical center line then sketching what would become the outer of the spinner, off setting the sketch to 1.5mm and using the revolve tool to create the solid, I added some holes to secure the motor, and designed in the void for the 6mm x 6mm momentary switch.

I designed a battery holder for the 9v battery and a screw in lid for the spinner.

I embossed "LAUNCH CONTROL" adjacent to the switch as well as the Pi symbol to the top surface of the lid.

The crank adapter is a snug push fit, this could be secured with epoxy resin or CA glue if needed.

Note: I made 2 of the Launchers with Identical 12v motors but one is clearly more powerful than the other.

The Conclusion and Results.

After designing and printing many spinning tops of various shapes and sizes, I found that there is clear evidence that tops with a lower center of gravity and greater mass to the outer edge created the longer and more stable spin along with the better times especially with powered spins times.

The 6.3mm steel ball seemed to work better then the 5mm ceramic balls, and with this knowledge in my armoury we could design tops using this method.

Another key part of this project was what surface to spin the tops on, the 3.5 minute manual spin was on a Porcelain side plate and the 10 minute Powered spin on the metal Lid of a Jar of unopened Lemon Curd,( I kid you not) the lid had a concave center and worked really well with the steel ball, then my wife opened the jar and what was once concave was now convex, which didn't work as well, all was not lost as I found an unopened Jar of Raspberry Jam with the same type of lid, we were back in business :))

Using steel balls improved spin time dramatically and at the end of this project we could expect over 3 minutes spin time with manual finger twist spins and up to 8-10 minutes with the powered spin which I thought was pretty good.

With the powered spin, I thought that holding the spinner on the top to reach full RPM would be detrimental to a longer spin, but this wasn't the case, the initial burst of energy and release worked just as well if not better, same applied to the manual spin, a quick twist of the fingers produced a better result.

This was a very rewarding and fun project to be involved with and it proved that using Science and in particular Physics and Pi we could produce tops with a longer spin time.

The powered launcher works really well and is great fun to use, print a couple of these off and some tops and you have a ready made game on who can achieve the longest spin times etc, there is definitely a knack to spinning a top and this was evident during the testing period.

Print files are included for the top with the best spin time and the powered spinner and crank release adapters.

Thanks for Looking.

Safety.

⚠️ Safety Consideration

While spinning tops are generally safe and popular with younger users, the motorized spin launcher in this project is designed for adult use or supervised environments only. Due to the high rotational speed and mechanical release mechanism, there is potential for friction burns or minor injuries if hands or fingers come into contact with the spinning top or launcher at speed.

To mitigate risks:

  1. All testing is conducted with proper safety precautions.
  2. Users are instructed to avoid touching the top while it is in motion.
  3. The launcher mechanism is enclosed and features a momentary switch to ensure precise control.

The tops themselves are designed with rounded edges and durable materials, and the threaded spindle system allows safe swapping without tools.

Safety is a top priority, and this project emphasizes responsible use of high-speed mechanisms to ensure a safe and enjoyable experience.