Swinging a Hollow Tube vs. Solid Cylinder

[gibberingmouther]

I know hollow tubes have bigger moments of inertia than solid cylinders, assuming their masses are the same.

But which one would swing better if you used it like a sword? I'm thinking that the tube would be harder to get moving but would have more rotational momentum and thus be harder to stop.

Is this correct?

I want to know for my tabletop RPG game manual which mentions lightsabers.

 

[phinds]

I'm thinking that the tube would be harder to get moving but would have more rotational momentum and thus be harder to stop.

And why do you think that? Can you back it up with math?

 

[trurle]

Mostly incorrect. The rotational inertia of slender object do not change much during thrusting and slashing movement, if you make weapon hollow (assuming the mass is kept). To make the effect count, you need to screw your weapon into target.

Weaponized impact driver?

 

[gibberingmouther]

And why do you think that? Can you back it up with math?

No, I cannot. I know the math for rotational motion but I don't know how to apply it to a person swinging a hollow or solid tube. I was just guessing, which for me is often helpful as a first step. I'm about to take my second course in physics … I'm not quite an expert yet.

 

[phinds]

No, I cannot. I know the math for rotational motion but I don't know how to apply it to a person swinging a hollow or solid tube. I was just guessing, which for me is often helpful as a first step. I'm about to take my second course in physics … I'm not quite an expert yet.

Under rotation it matters whether what the organization of the matter is based on the axis of rotation. So when you rotate a cylinder about it's long axis, it matters.

When you are swinging a baseball bat, for example, why would it matter whether it was hollow or solid as long as the average density was the same since you would be swinging it about an axis that sees even distribution of matter.

 

[DaveC426913]

Why would a hollow cylinder behave differently than a solid cylinder of the same mass?

 

[phinds]

Why would a hollow cylinder behave differently than a solid cylinder of the same mass?

If rotated about it's long axis, a solid cylinder would have a different rotational inertia than one where the mass was concentrated in the shell. For example, If you took a tin can that was solid and another of identical size and weight that had a thick shell and a hollow core and put them on an inclined plane and let them go, the hollow one would be slower to start and slower to roll down the plane because of greater rotational inertia.

 

[DaveC426913]

If rotated about it's long axis, a solid cylinder would have a different rotational inertia than one where the mass was concentrated in the shell.

OK, sure. But the OP was talking about swinging it like a sword.

 

[phinds]

OK, sure. But the OP was talking about swinging it like a sword.

Right. Which is NOT swinging it about the axis of asymmetry, as I have already pointed out.

 

[RPinPA]

Agreeing with all of the above saying "same moment of inertia" but putting a little bit of math behind it. Moment of inertia is a sum of $mr^2$ for each piece of pass $m$ where $r$ is the distance from the point of rotation. For these two cylinders of the same mass rotating around their endpoints, any piece at a given distance from the end is going to have the same mass for both. The sums are the same. The moments of inertia are the same.

To the OP: It's the mass distribution that matters in terms of distance from the hilt. Adding mass farther away from the hilt increases the moment of inertia more than mass close in, and causes the same overall mass to be harder to swing but also carry more energy (and thus do more damage).

 

[Tiran]

Hollow tube has more wind resistance, assuming that it is a larger diameter. It isn't clear how the two tubes are actually different.

 

[phinds]

Hollow tube has more wind resistance, assuming that it is a larger diameter. It isn't clear how the two tubes are actually different.

But we are not assuming that it has a larger diameter. How the tubes are different has been fully discussed in this thread. What part did you not understand?

 

[Tiran]

But we are not assuming that it has a larger diameter. How the tubes are different has been fully discussed in this thread. What part did you not understand?

You'll need to quote exactly where in the thread the OP said the hollow cylinder is a different density material than the solid.

Do you understand that your mental assumptions aren't actually on display in the thread?

 

[phinds]

You'll need to quote exactly where in the thread the OP said the hollow cylinder is a different density material than the solid.

Do you understand that your mental assumptions aren't actually on display in the thread?

OOPS. You are correct. Nowhere is it explicitly stated that everyone is talking about same diameter cylinders and the rest of the discussion is based on that assumption.

 

[DaveC426913]

Differing diameters occurred to me too.

But I think, generally - unless specifically called out otherwise - all factors need to be considered comparable.

I mean, no one specifically stated that both bars are not permeated with holes (another way of changing mass without changing diameter).

There are an indeterminate number of factors that could come into play here. We must assume them all to be equivalent until called out explicitly.Still, it's good that Tiran pointed it out. It's also good that, since he did inject a changed factor, he called it out as an assumption.

 

[Tiran]

Differing diameters occurred to me too.

But I think, generally - unless specifically called out otherwise - all factors should be considered comparable.

I mean, no one specifically stated that both bars are not permeated with holes (another way of changing mass without changing diameter). There are an indeterminate number of factors that could come into play here. We must assume them all to be equivalent until called out explicitly.

There is no way for tube and rod to be "comparable" in the way you mean. Either they are made of comparable materials of the same density and different geometry, or they are made of different, non-comparable materials of different densities. I don't know why anyone would assume geometry or density would be a more natural variable - they are both variables.

 

[DaveC426913]

There is no way for tube and rod to be "comparable" in the way you mean. Either they are made of comparable materials of the same density and different geometry, or they are made of different, non-comparable materials of different densities. I don't know why anyone would assume geometry or density would be a more natural variable - they are both variables.

You assumed that both bars had solid surfaces. You assumed that it didn't have its mass modified by a perforated surface - rather than by diameter.

If I had the time, I might come up with a few more factors we are all (including you) assuming are equivalent between the two bars - because we just haven't thought of them yet.

The number of assumptions we must make just to answer the question is indeterminate - it can't be listed.

Therefore, the only way to meaningfully answer the question is to assume all factors except those explicitly mentioned are the same between the two bars.But I'm not disagreeing with you. You did explicitly call out your assumption.
But you're getting into a practical territory of how it might be different.

My whiffle bat is another way, but I can't claim the OP had to state the bars are not made of whifflium.

 

[Tiran]

You assumed that both bars had solid surfaces. You assumed that it didn't have its mass modified by a perforated surface - rather than by diameter.

If I had the time, I might come up with a few more factors we are all (including you) assuming are equivalent between the two bars - because we just haven't thought of them yet.

The number of assumptions we must make just to answer the question is indeterminate - it can't be listed.

Therefore, the only way to meaningfully answer the question is to assume all factors except those explicitly mentioned are the same between the two bars.

Sure. So why did you automatically assume the tube was denser and I first assumed it was the same material but larger? Neither one is more or less likely given the parameters, and both are more likely than introducing a new detail like a perforated surface that could apply to either.

If you went to a hardware store and said you needed a rod and a tube of the same length and weight, you would not be supplied with lead tube and a steel rod. They would hand you a narrow rod of steel and a wider piece of steel conduit. If you objected to their differing diameter, they would ask if the rod could be a dowel, because lead pipes aren't common and aluminum rods aren't so low in density that they will be as light as conduit.

The thread is mainly interesting because it illustrates how people jump to conclusions - probably based on what sort of activities they do. I make things, so changing both density and diameter - like on a steel vs aluminum bicycle frame - are going to be natural variables.

 

[DaveC426913]

Sure. So why did you automatically assume the tube was denser

Actually, I'm not sure anyone assumed the tube was denser. I'd have to check.

You don't really have to make any assumptions about how the hollow bar masses the same as the solid bar, just that it does. Granted, most solutions will require knowing.

 

[Tiran]

Actually, I'm not sure anyone assumed the tube was denser. I'd have to check.

You don't really have to make any assumptions about how the hollow bar masses the same as the solid bar, just that it does. Granted, most solutions will require knowing.

How are a bar and a tube of the same mass, length and diameter going to be anything but different densities?

 

[gibberingmouther]

Just to clarify, this was for lightsaber design in a tabletop dice rpg, so the diameters would be the same. The magic Force particles the lightsabers are made of could have whatever mass is desired, thus any density. I just wanted a description of the lightsaber that sort of makes internal sense.

I'm probably going to stick with a "tube" lightsaber because of the energy cost most likely being lower. I mean, unless we somehow grow giant brains merged with computers in the future (and I don't think that's ever going to happen!) … I don't think we'll ever be able to "design" a dream world like I talk about in my game manual. My logic for how magic, the Force, or psychic abilities work is based on the idea of many minds being in a shared dream with each other, but with some minds (such as the gods, or the top deity I call the "game master", which is also the role for the person who is in charge of the game) having more ability to do "reality warping" on the dream than others.

This "dream world metaphysics" for my rpg is based on me personally being a very vivid dreamer … and on the idea that even our reality might be some kind of dream given by God. I have nothing to back up the latter idea, and to me it's just a possibility - I have no divine revelation or anything that let's me know whether it could be true or not. I do happen to believe in God … but that's kind of besides the point for a discussion about physics and game design.

 

[Tiran]

The magic Force particles the lightsabers are made of could have whatever mass is desired, thus any density.

If it can have any mass, why are you asking about inertia?

 

[gibberingmouther]

If it can have any mass, why are you asking about inertia?

My paragraphs about the Force and lightsabers in my game manual were mainly just an aside, so I didn't bother trying to work out a lot of details for everything I talked about.

I assume more mass has an energy cost in this game world. I wanted to know what the most efficient design for a lightsaber would be - a tube is perfectly fine for burning through stuff and would seem to be better since it has a lower energy cost than a solid blade. If however a solid blade would swing better and be better for dueling, then the Jedi might prefer that design for their lightsabers. So, it's a matter of what the most efficient design would be.

I don't think I would have even thought about this if I hadn't been taking a physics course where we talked about rotational motion and rotational inertia. I mistakenly made an association between tubes having a bigger moment of inertia than cylinders (given the same mass) and thinking this might have an effect on swinging a lightsaber.