How quickly is motion transferred in a solid object?

Question

Just for example: assume an iron bar one foot in length. If you push on one end, the entire bar will move. This seems instantaneous. but actually, from my understanding, the atoms all push against each other in a very fast "wave" - making the entire bar move.

Now, say the bar is 2 light-years long. We are at one end of the bar, and rotate it 90 degrees. Clarification: rotation is the same as if you held a pencil horizontally by the eraser, then turned it vertical. This seems to mean the other end of the bar stays where it started until our motion travels through the entire bar. How long would that take?

Answer 1

This is actually a really interesting question, but the answer is simpler than you might think. The pressure wave propagates along the bar at the speed of sound in whatever material the bar is made of. This is because sound is nothing more than pressure waves, and so the speed of sound is by definition exactly what you're looking for.

For example, the speed of sound in iron is around 5130 m/s (from this site), so any disturbances would propagate along the bar at that speed.

Answer 2

You can grab on end and pull it or push it, but since you want to rotate it, and you have to travel a quarter circle of a 1 light year radius circle, it's going to take you more than $2\pi /4$ years to get your end into position.

And as you grab your end each part of the rest of the bar stays at rest until the pressure is transmitted from your hand through the bar to the part in question, and pressure waves travel at the speed of sound since sound is a pressure wave. You can choose to move at less than the speed of sound in the bar yourself to give it a chance to try to move somewhat together. If you move your end faster then bar must and will deform, so you can imagine that you have to pull quite hard. The faster you try to move it, the more it will deform and the harder it gets. Deform it too much and it can even break.

And if you try to stop turning it after the 90 degree turn that stop will also take time to propagate. And when you deform it it can start to wobble, it's a bit like moving a slinkly or a rolled out piece of playdough, you might even lose some energy to heat as the speed of sound itself can vary as the objects deforms enough to change it's density. So you might end up with a vibrating bar despite your best efforts.

Another thing to consider about a bar that large is that it might self gravitate as well.