If an object is placed at the end of of a VERY long bar that is connected to an axel, Could rotating the bar close to the axel make the object at the other move extremely fast (like light speed)?

Submitted by Swade060504 t3_101um7u in askscience

So my son came up with a hypothetical experiment about a beam that cannot flex and is incredibly long. The beam is placed such that it connects to an axel with a small portion extending past the axel on the other side (think watch hand). Also imagine the whole thing is in space. Could a spacecraft placed at the end farthest away from the axel be propelled to light speed by rotating the short piece on the other side the axel a short distance?

I think I know that a point moves faster the farther away from the axel because it must keep up with all points closer but has farther to move. Other than this I am lost. This came after talking about about levers and Archimedes quote about moving the world with a long enough lever. P.S. I told him I don't think it would reach light speed but I am unsure as to why except that if this were true it would be common knowledge by now.

Thank you for your response

Stumped Dad

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Weed_O_Whirler t1_j2sb2h7 wrote

Everything you're saying holds up, except for this one thing:

> a beam that cannot flex and is incredibly long

In physics, we often times talk about "rigid bodies" and make the assumptions that they are infinitely stiff, but that's just a "small thing, moving slow" assumption- where they appear to be completely rigid. In real life, materials are not completely rigid.

Now, you might think "that's just an engineering problem, we can just design something to be really stiff. But you can't. Information- including compressions and rotations, travel through a material at that material's speed of sound. Which makes sense if you think about it, sound waves are compressions passing through a material.

So, if you had a really long rod, and you started rotating it faster and faster, the rod would start to bend and then shear. And that's not an engineering problem- it's a real physics one.

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SW_Zwom t1_j2sdh2u wrote

I was actually asking myself this: If the rod did not bend at all - could we even move it? I mean without any pressure wave travelling through the material it could not accelerate. So wouldn't perfect rigidity require an infinite speed of sound inside the material? That would make it impossible, even in a "ideal" calculation...

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die_kuestenwache t1_j2t0rp6 wrote

In principle, yes. Infinite rigidity would mean infinite speed of sound. As soon as the velocity of any part of the rod approaches the speed of light, the torque necessry to further accelerate the rod would go towards infinity. However, as others have pointed out, infinite rigidity violates relativity as the speed of sound itself cannot exceed the speed of light.

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solenyaPDX t1_j2t00wt wrote

Even if we assume a non flexing support rod, you'd need to apply torque to the axle to move the object. The energy required to move the object wouldn't change, so you'd be looking at infinite torque necessary to turn the axle.

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OverJohn t1_j2swp18 wrote

Rigidity and relativity is more complicated than you might think.

Firstly, relativity constrains the speed of sound in an object. This means for example you cannot have a rigid pole where pushing one end causes the other end to move instantaneously.

Secondly, relativity constrains rigidity even further. We could conspire to apply forces across an object at the same time in its instantaneous rest frame such that the object never experiences deformation in its rest frame. When we do this the object is called "Born rigid" (after Max Born). However it turns out it is impossible to for an object to be Born rigid under all types of motion. The motion in your son's hypothetical experiment would be an example of a type of motion where it is impossible to even maintain Born rigidity.

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rootofallworlds t1_j3207ah wrote

In classical mechanics, if the stiffness (ie the relevant elastic moduli for the wave type) tends to infinity or the density tends to zero then the speed of sound tends to infinity. Am I correct to think that when you apply special relativity, the speed of sound would tend to c and not infinity in those limits?

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PennyG t1_j3kfbh8 wrote

Nice explanation. If an object (like a very long steel rod) could be infinitely rigid, you could communicate information faster than the speed of light, which is obviously not gonna happen.

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