Converting Rotational Force to Linear Momentum: The Coupled System

The Core Objective

The core objective of this post is to test the conversion of rotational force to linear momentum, and to demonstrate how this might be accomplished internally for a space environment. We will be doing this with two separate experiments called Experiment 1 and Experiment 2.

These two experiments must be viewed together as a single coupled system. Experiment 1 shows how rotational force converts to linear momentum using external constraints, while Experiment 2 proves those exact same constraint conditions can be replicated internally.

Experiment 1: External Constraints & Baseline

Experiment 1 consists of a single spinning scooter wheel mounted on a bolt for an axle. A line is attached to this axle, and the wheel is suspended from a two-pulley and counterweight system. This setup allows us to observe its horizontal precession and, more importantly, to see how cutting off that rotation translates precessional force into linear momentum.

Key Cruxes of Experiment 1

• The Stationary Pivot: The pivot is the fishing line connected to the end of the axle opposite the wheel. You will notice that the pivot does not move nearly as much as the precessing wheel does in the opposite direction, if at all. It remains positionally stationary, which is one of the crucial behaviors we must observe in both experiments.
• Momentum Conversion: When we cut off that horizontal rotation (gyroscopic precession), this is the point where rotational force converts and translates into linear momentum along a straight tangential path. This conversion is made possible by the external constraints of the setup.

Experiment 1: External Constraint Precession Demonstration

Key Observation: Watch the single gyroscope precess horizontally around the stationary pivot, translating angular momentum into linear displacement along the constrained path.

This fundamental concept is exactly like spinning a rock around on a string: the hand (an external force) keeps the rock in a circular orbit. The moment you let go of the string, the rock flies off at high speed in a straight line, pulling the string along with it. In Experiment 1, cutting off the gyroscopic precession acts just like letting go of that string, allowing the rotational energy to translate cleanly into a straight linear path.

Experiment 2: Internal Constraints

This brings us to Experiment 2. The setup here is simple: two counter-rotating scooter wheels mounted to a central hub. We horizontally rotate these wheels by hand, causing them to precess upwards and outwards simultaneously.

Experiment 2: Internal Constraint Precession Demonstration

Key Observation: Watch the twin counter-rotating wheels precess upwards and outwards on their pivots, demonstrating internal constraint dynamics identical to Experiment 1.

The point of Experiment 2 is to prove that two scooter wheels can constrain each other internally in the exact same way that a single wheel is constrained externally in Experiment 1. The mechanical results of the internal and external forces are identical.

You might notice that in the physical demonstration, my hand provides the horizontal rotation, which is technically an external force. This manual input is simply a practical prototyping technique to provide the necessary horizontal torque. In a deployed space environment, an internal electric motor pushing off a central stator performs this exact same mechanical function. An internal motor can do exactly what the external hand does to initiate the rotation.

To replicate the external constraints internally, we simply use two counter-rotating gyroscopes with two separate pivots connected to a common hub. If an internal motor were rotating both gyros horizontally, there would be two counter-torques (anti-torque reactions) acting directly on the motor.

Top-down schematic illustrating the symmetrical, opposing anti-torque reaction paths generated between the central motor-driven hub and the dual scooter wheels

Because these two anti-torque reactions oppose each other exactly, they cancel out perfectly at the hub. As a result, the center remains perfectly stationary in space while the gyros rotate around it in opposite directions.

This reveals the core connection: Experiment 1 uses the external environment (gravity pulling down, a string pulling up) to hold the center still. Experiment 2 uses internal symmetry (two wheels perfectly balancing each other's torque) to hold the center still. The external constraints of Experiment 1 achieve the exact same mechanical result at the hub as the internal constraints of Experiment 2.

Synthesis: Why Experiments 1 & 2 Must Be Evaluated Together

If we evaluate either experiment in isolation, it could lead to incomplete conclusions because we wouldn't see how both sets of constraints yield identical results. Experiment 1 demonstrates how precessional motion converts into linear force under external constraints. Experiment 2 demonstrates how internal constraints can produce that exact same precessional behavior. Viewing them together allows us to observe how internal mechanics can flawlessly replicate external constraint conditions.

When viewed as a single coupled system, we combine the two principles: the conversion of rotational force to linear force (Experiment 1), and the self-contained internal constraints (Experiment 2). In a closed system in space, we can drive both counter-rotating wheels to precess upwards and outwards. By abruptly interrupting that horizontal rotation within this closed system, we create a clear empirical test to observe whether precessional energy translates into linear momentum, allowing us to test for net translation of the entire system through space.

With a clear understanding of what we are observing in each experiment and why they form a coupled system, we are ready to build. Let's move on to the replication instructions so you can test and see this for yourself.

Experiment 1 Build Instructions & Materials

So, we will begin with Experiment 1 and how to put that together. You don't have to follow these exact materials, but these are the materials that I used. If you have better materials or access to machining or high-grade laboratory equipment, then by all means use that instead if you feel so inclined. But these two experiments can be built with hardware store materials as well.

The Frame and Pulleys

Experiment 1 consists basically of two pulleys that are hanging on a long wooden board roughly 21" apart. If you can find a long, straight 2x4, then that would work and is actually much sturdier. I used a 2-1/2" wide x 3/4" thick x 6' long pine board simply because it was flatter and straighter. I simply laid that across two tall shelves that are about 4 feet 4-1/4 inches high off the ground.

For the pulleys, you don't want to get these from the hardware store. They are absolute garbage for this and the wheels use a simple hole for a simple pivot and are more for lifting big dumb things. For Experiment 1, you will want pulleys with easy-rolling bearings in them. I sourced mine from Amazon. You can use this search term: "Groove Pulley Wheel for Rope Wall Mounted 2 Pack Stainless Steel Super Silent Cable Pulleys Wheels System V Type Blocks Rollers Detachable Duplex Bearing for Gym Equipment Sliding Gate (with Screws)".

Oddly enough, it's actually cheaper to get the two-pulley set with the screws. The screws are garbage and you can just throw those away. I just used 1/4"-20 stainless steel bolts (1-1/4" long) with lock nuts and washers of the same size. You might need longer bolts though if you have a thicker wooden board. There were 8 holes total for both pulleys, so a total of 8 bolts, washers, and locknuts.

When looking for the pulleys make sure they have that perfect V shape in them to hold the line on. That way the line doesn't fall off easily. The U shape should work too but is more for a thicker rope or string. You may find other pulleys with different sizes and numbers of holes, however. But the important thing is that they must have bearings in them!

Also make sure that they come with detachable bearings. The pulley bearings can sometimes be garbage too and are good enough as-is for Experiment 1, but can always be upgraded if you find pulleys with detachable bearing. They don't always tell you what kind of bearings come with the pulleys in the descriptions. But the bearings that came with the pulleys I found were actually 6000Z single metal-shielded ball bearings (10 mm bore × 26 mm outer diameter × 8 mm width).

The Counterweight Assembly

For the counterweight, I used a 6 lb. workout weight (the kind with the hole in the center), fender washers, stainless steel nuts, and dies, all on a 5/16"-18 zinc-plated hex bolt. This is around a total of 3328g, or about 7 lb. The stack goes like this, starting from the bottom:

• Head of the hex bolt
• 5 or 6 stainless steel fender washers
• The 6 lb. weight
• Two dies used for making rings out of coins
• Six more fender washers
• Two stainless steel nuts
• Another stainless steel nut tightened up against a nut coupler

You don't have to use ring making dies. I just already had those on hand so I used them. You can just as easily use nothing but washers, nuts, nut couplers, etc. and achieve whatever weight that you want. I simply placed a pillow on a crate to catch the counterweight when it falls and makes an impact.

I drilled a tiny 5/64" hole into two opposite flat sides of the nut coupler. Then I used a countersink bit to carve out a slight bevel in the holes, twisting it by hand. This is so that the line doesn't easily get cut on the edges of the holes and snap. But you could probably get away without countersinking a bevel.

The Gyroscope Wheel Assembly

Then we have the scooter wheel that will act as a gyroscope. Any standard sized scooter wheel will work and you can get them anywhere. If you feel so inclined you can try metal and I would love to see how that performs! We put this on a 5/16"-18 zinc-plated hex bolt (5" long) that acts as the axle. The stack goes like this:

• The head of the hex bolt
• A fender washer
• A speed washer (the small ones that come with the trucks of a skateboard)
• A bearing
• A bearing spacer that goes inside of the wheel
• A bearing
• A speed washer
• A fender washer
• Two stainless steel nuts that act as jam nuts
• Two nylon nuts on the very end sandwiching and clamping the line

I use skateboard bearings because they have an 8mm inner diameter inside of the inner race. A 5/16" bolt measures roughly 7.94mm and they fit perfectly inside of the 8mm inner race with almost no slop. And you can easily get these from your local Lowes or Home Depot store. You can use any 608 or standard ABEC 5 skateboard bearing. But for a really good, near-frictionless bearing, I used Bones Swiss Ceramic skateboard ball bearings. But the cheaper Bones Reds work just as well and are also of good quality that has a really nice spin.

When tightening the washers against the inner race of the bearings, you don't want to tighten those super tight. You want some slight looseness there, but not too much. This is so that the spinning wheel doesn't also turn the inner race and make the axle and line vibrate when the wheel is precessing.

You want to be able to grab the wheel with one hand and rotate it back and forth without the axle moving at all; a little movement is ok though. A good indicator that you have just the right amount of tightness is that the fender washers should be able to rotate. The fender washers also act as umbrellas to protect the line from getting sucked into the air vortex of the spinning bearings and snapping the line.

Setting Up the Apparatus

Ok, so now we must run this experiment so we can see the horizontal rotational precession convert into tangential linear momentum horizontally. In other words, we are going to witness the rotation of precession convert into horizontal travel.

Rigging the System

I used Berkley Trilene Big Game Ocean Blue Braided 65 lb. fishing line. This is excellent for strength but can get sliced easily, so you have to be careful of that. I chose this line not only because of its strength but also because it swivels well and doesn't have memory, so it can twist several times over without a hitch. The only caveat is that you will have to order it online to get a color that actually contrasts against the background if you are recording.

Next, we tie the line onto both the counterweight and the axle of the wheel. Make sure you have the line going through both pulleys first! You can use any knot really, but I find the uni knot works well and is superior. A quick YouTube search will reveal lots of videos on YouTube on how to tie a uni knot. Just slip the line through the holes of the nut coupler on the counterweight, then tie the knot. For the wheel, just tie a knot on the end of the axle furthest from the wheel and use the nylon nuts as a clamp to hold it on even better.

Depending on how high you positioned the pulleys from the floor, the counterweight has to be at just the right height so when it lands, the wheel doesn't go slamming into the pulley directly above it. You may have to adjust the length of the fishing line and raise the height of where the counterweight lands.

I find with my specified height between the floor and pulleys that a crate with a pillow on top provides just the right landing pad. You want both the counterweight and the wheel hanging roughly at the same height. They should be hanging evenly, slightly below the halfway point between the pulleys and the floor, and just above the crate and pillow.

Securing the Counterweight

Before we can spin up the wheel, we need a way to hold the counterweight up and clamp the line so that everything stays in place. I actually had issues with this and finally had to settle for a 6" Irwin Quick-Grip clamp. It seemed like an attractive solution at first, and it did work—at least for a little while.

I clamped it directly over the line, pressing it right up against the pine board structure. To drop the weight, I would just pull the quick-release trigger. Although it worked long enough to record the videos, the counterweight soon began to slide downwards on subsequent runs. What happened was that the thin braided line ended up creating a depression in both the rubber padding of the clamp and the pine wood.

Because I clamped it in the exact same spot over and over, the line would slip into these grooves and slide through, causing the weight to drop prematurely. I had to squeeze the clamp incredibly hard to get it to grip the line and keep the 7 lb. weight held up. Because I had to squeeze it so hard, it also made it very difficult to hit the release trigger without shaking the setup.

I did try an alternative: a Marlinespike Hitch, where you stick a pin through a knot on the line. When you pull the pin out, the knot magically disappears and drops the counterweight. However, because of the 7 lb. weight and the thin Trilene fishing line, the line wrapped too tightly around the pin, making it hard to pull out.

So, you might want to find a better solution for this. Even placing a simple trap door underneath the counterweight with a quick mechanical release would work perfectly. I only used the Irwin clamp because I needed a quick solution. I also needed for all the moving parts to be fully visible for the camera.

Spinning Up the Gyroscope

Once the weight is secured, the first thing we have to do is spin up the wheel. For that, I use a rotor from an RC plane motor chucked into a Dremel. The larger diameter of the rotor helps get more RPMs out of the scooter wheel.

I realize that not everybody has an RC plane motor just laying around, so you might have to come up with a different solution for fitting something with a larger diameter onto a Dremel. It doesn't even have to be a Dremel; any high-speed rotary tool you have will do. The point is you just need something to spin the scooter wheels up.

If it comes down to it, you can always just use the standard rubber mandrel for a Dremel (the one the sanding bands go on). It has a smaller diameter and therefore won't get your scooter wheel spinning at blinding speeds, but it will get it spinning regardless. High speeds on a scooter wheel are great, but a lower speed is okay and will still accomplish the job. I will explain why slower speeds can actually be even better further down below.

Operational Procedure

The core idea is that we have to raise the counterweight up to a certain height and lower the wheel close to the floor and clamp it there. Then we simply release the counterweight so it drops and the wheel goes shooting upwards.

Here is the order of the process:

1. Raise the counterweight up and hold it down with the wheel resting all the way down near the floor.
2. Spin up the wheel with the Dremel, then let it go so it begins precessing around the pivot.
3. Release the counterweight to drop. This pulls upwards on the pivot of the wheel, which causes a quick downwards tilt. Think of it sort of like amplifying gravity where it tilts the axle more than what gravity alone can do.
4. Consequently, this speeds up the precession in a quick burst. The now-precessing wheel goes shooting directly upwards.
5. The counterweight lands on the pillow, which will cut off the precession of the wheel. The wheel will still have some upwards momentum and make the line go slack directly above it.

Just at this moment, when the counterweight lands and the precession stops, we will now see a conversion from precession to a horizontal translation of the wheel due to inertial and tangential linear momentum. The wheel will then take off horizontally to the side pulling the slack line along with it. Just think of it as spinning a rock around with a string and then letting go of the string; the rock takes off in a straight line pulling the string along with it!

Fine-Tuning & Key Observations

Here are some general rules of thumb that I have discovered to help fine-tune this to get a nice horizontal linear take off. The goal is to speed up the precession of the wheel so that it orbits around the pivot, while the pivot itself rotates in one place and remains mostly stationary in position.

• Shorten the Axle to Stop Pivot Coning: If your pivot is drawing a huge cone path in the air and wandering out of position, your axle bolt is too long. I initially started with a long bolt at max RPM, but the extra leverage caused too much inertia and pulled the line out into an ugly cone too early. I found myself rushing to release the counterweight before it had time to pull the line and wheel out too far. Shortening the axle bolt solves this by keeping the pivot anchored firmly in one spot.
• The Leverage vs. Travel Trade-Off: Keep in mind that a shorter axle acts like a shorter lever arm, meaning the counterweight won't be able to tilt it as aggressively. You will sacrifice some of that flashy horizontal travel distance, but keeping the pivot rock-solid in space is far more important for proving the baseline mechanics.
• Timing the Spin-Down "Sweet Spot": Because a shorter axle is harder to tilt at blinding RPMs, don't drop the counterweight immediately after spinning it up. Let bearing friction naturally decay the wheel speed until you see the pivot just beginning to move out of place. The moment it hits that friction sweet spot, release the counterweight—the pivot will stay locked in place right as the wheel takes off in a horizontal translation.

There are a few things that we need to be watching for in order to see the relevance of the experiment:

• Pivot Stability: We are watching for how the pivot (where the line connects to the end of the axle) will not move out of its positional place as the wheel orbits around it. This in and of itself is remarkably phenomenal. The pivot is totally and completely free to move horizontally where gravity does not act horizontally but only vertically.
• Horizontal Translation: The next thing to watch for is the horizontal movement of the wheel when its gyroscopic force is cut off. This basically makes a near-perfect space simulation when we are watching for any horizontal movement of either the pivot or the wheel.

Experiment 2 Build Instructions & Materials

Ok now it's time to move on to Experiment 2. This setup isn't much different than the setup of Experiment 1. What we have done is add another scooter wheel, pivots, a hub (a skateboard wheel) and axles to make a counterrotating apparatus. Don't worry there aren't any pulleys or falling counterweights in this one!

The Hub

Let's start with the hub. For that I simply used a 53mm Ricta Chrome Core 101A Wide skateboard wheel. I don't think they make those anymore but you can use any 53mm skateboard wheel from a skateboard shop like Zumies or from online. The harder the durometer the better. A 53mm wheel is just the right size for the pivots to fit around.

I drilled two equidistant holes on each side using a #7 (or 13/64") drill bit, then hand-tapped them with a 1/4”-20 tap. This allows you to secure the pivots directly to the hub using two 1-1/4” long, 1/4”-20 stainless steel bolts.

You can use longer bolts if you want. It's a a good idea if you want to rotate the hub and wheels around much easier. Longer bolts will give you something to push on when rotating the counterrotating wheels around horizontally.

The Pivots

The next thing are the pivots. For this I used clevis hangers. I sourced two 2-inch Clevis Hangers (from Lowe's). These come with a 1/4”-20 x 3-1/4” bolt. I totally ditched the halves with the straight sides on them and used only the curved halves. They already have holes on the sides and that's where the 1/4"-20 bolts go through in order to attach them to the hub. You also don't need the 1/4" bolt that comes with the clevis hangers.

However, you will have to drill out a hole in each clevis half right at the center of their curves. These holes should be drilled out with a 5/16" drill bit. This is so that you can attach the axles (5/16" hex bolts) of your wheels to the clevis pivots. Use nuts on each side of the curve to attach the axles to the clevis pivots.

The Counterrotating Scooter Wheels

The next thing are the scooter wheels assembly. We will setup the wheels similar to The Gyroscope Wheel Assembly section. So you can simply refer back to that section for bearings, hex bolt for the axle, nuts, washers etc.

It's up to you whether or not you want to add fender washers or not but there isn't any real need to. I didn't use fender washers. I simply placed the scooter wheels and their bearings on a 5/16"-18 zinc plated hex bolt and held them on with nuts. Lock nuts don't work so well for this so stick with two nuts tightened against each other. Two regular nuts will lock just as good as a single lock nut. For the hex bolts or axles you can use stainless steel or threaded nylon rods too if you prefer.

I do suggest placing the speed washers on though even though you don't really need them. Speed washers are just those tiny washers that come with the trucks that go on the skateboard. The diameter is sized exactly to the inner races of the bearings. So that way you can't ever overtighten the nuts onto the bearings. Instead you would be tightening the speed washers on to the inner race of the bearings only.

Just like in the Experiment 1, you will need bearings and I mainly use skateboard bearings. They fit the best on the 5/16" axles. So now it's time to attach those axles to the clevis pivots. This is straight forward, you simply take the hex bolt axles and slip them through the holes we drilled earlier. Tighten with double nuts on each side of the curve. If you're feeling particularly lazy a single nut tightened on each side works just as well, but they will eventually loosen.

The Gyro Holders

This wouldn't be complete without mentioning the gyro holder. These are what hold the scooter wheels and pivots up for you. They aren't absolutely necessary but we are talking about a minimalist setup here where the wheels aren't geared to spin together. So you may find it hard to get the wheels to spin at the same speed all the time during your testing. And you may get tired of holding both wheels in some weird way while trying to spin both of them up at the same time. And then trying to horizontally rotate them equally on top of that can be a real pain.

However you may only need to see this once and you just might manage to get it right the first time. But just in case, I used two 3/4" wide, 1/8" thick and 3" long aluminum bars. These bars are bent in such a way that they hold the wheels and pivots at roughly 45° angles below the horizontal. You really want your wheels to be held up anywhere from 45° below the horizontal to the horizontal. When the wheels are horizontally lined up with the hub then that's the horizontal. The reasoning for this is so that we have plenty of room to watch our wheels precess upwards and outwards.

Alternatively, you can choose to start right at the horizontal where the wheels line up directly with the hub height—it's entirely up to your personal preference and how you want to stage your test. But if you want to start from the horizontal just make sure your aluminum bars are bent to hold them up at that angle.

You will also have to drill two more holes in the hub at 90° angles to the pivot holes. Just like the pivot holes, use a #7 (or 13/64") drill bit, then hand-tap them with a 1/4”-20 tap. Then just drill 1/4" holes in the aluminum bars and screw short 1/4"-20 and 1/2" or 3/4" long bolts through the bars and into the hub. You will want to have the bolt head tightened right up against the aluminum bar. But don't overtighten because the hub is a hard plastic after all and we don't want to strip that out. You just want the tightness to be as snug as a bug in a rug.

The Stand

You will want to place the entire thing on something that can hold everything up. This doesn't matter too much and I used an acrylic plastic shaped like a large square. You can use wood just as well just as long as it's big enough to hold everything up and steady.

All you have to do is drill a 5/16" hole right in the center and place a long 5/16"-18 bolt or threaded rod through it. Then just slip your hub, wheels, pivots and axles onto this 5/16" bolt or threaded rod. If you need something longer you can always just use a threaded rod cut with a Dremel to size.

You'll want to be able to rest your wooden platform flat on a table. If using wood you can drill a smaller recessed hole on the bottom of the wooden board that's a little bigger than the bolt head. Or if using a threaded rod drill the hole a little bigger than the nut.

You can use a lock nut here because it would be right on the end of the bolt or rod inside of that small hole. Or you can simply raise the whole thing up using rubber furniture feet or bumper pads. Even simple bolt heads on each of the four corners would suffice.

You can spin on two nuts higher up on the bolt or rod and tighten them against each other. Then you can let the bearings inner race inside the skateboard wheel hub rest on these nuts. You will have something that looks similar to this:

An experimental setup featuring nylon axles, a socket-reinforced central rod to handle the lateral torque from line-pulling, and a spring resting on the lower nuts against the bearing's inner race to track vertical displacement.

Operational Procedure

Now all we have to do is spin up our scooter wheels. You can use the Dremel discussed earlier or whatever other rotatory tool that you decided to use. We must actually spin these in the same direction when facing each wheel. When spinning they will look like they are counter rotating, one up and one down, when viewing at the same time. The easiest way to do this is have one wheel in front of you and spin it up. Then rotate the whole thing on the hub to get the other wheel in front of you and spin it up in the exact same way.

And this is the last step, I promise. Once you get the wheels spinning you simply rotate the whole thing horizontally by pushing on a bolt sticking out of the hub. What you should now see are both wheels precessing on their pivots, upwards and outwards. If one wheel or both wheels precesses downwards then you have spun them in the wrong direction.

Key Observations

This is the point where we want to see the internal constraints that are actively lifting the wheels upwards and outwards. It is important to realize that the upwards and outwards precession of the wheels have the identical results of Experiment 1. It is equally important to realize that the hand is not needed to horizontally rotate these wheels. A motor in space can act as an internal constraint just as well as described elsewhere in this blog.

If you feel so inclined any number of ways could be used to check for the hub pushing downwards as the wheels precess upwards. But this is out of the realm of this simpler build but you can use a simple spring underneath the hub to check for this. If you have a laboratory environment you can use sensors or a highly accurate scale to check for any weight loss.

But this requires a way that doesn't require a hand to horizontally rotate the counterrotating wheels. An RC plane motor could do this, but again this is out of the realm of this minimalist build.

Well we have come to the conclusion of the Experiment 1 and Experiment 2 builds. Keep in mind the purpose of these two builds is to observe the External constraints of Experiment 1 and the Internal constraints of Experiment 2. We are testing that the results of these constraints are indeed identical to one another. The results being that each experiment when given an initial rotation result in the gyro/gyros orbiting around their respective pivot/hub.

Here is a way to help keep the perspectives correct. If you take Experiment 1 and rotate it upwards by 90° you will see that it matches Experiment 2. So when we see horizontal travel in Experiment 1 then rotated it 90° then it would look like Experiment 2 traveling vertically.

The internal constraints of Experiment 2 can be done with a motor. Not only that, a motor can precess these wheels in space in the same way they precess in Experiment 1. When these two experiments are viewed together we should consider the results of both the external and internal constraints. Then we should ask ourselves, "Gee, what if what I am seeing in Experiment 1 is indeed identical to Experiment 2? Then could the motorized Experiment 2 actually be able to travel through space?".

Experiments 1 & 2: Combined Coupled System Demonstration

Key Observation: Compare the external constraints of Experiment 1 directly alongside the internal counter-rotating constraints of Experiment 2 to observe how both systems achieve equivalent mechanical behavior.