# Relativistic motion

I've always found rotational motion a little weird...

The "odd" result is that a while a fixed linear force causes steady acceleration and an ever increasing speed with a fixed direction a fixed rotational force causes steady acceleration via a steady change in direction while speed remains constant. And that's because acceleration and velocity vectors are coincident in linear motion and offset 90 degrees with uniform rotational motion.

But as one "silly example" of how they may be different, linear acceleration doesn't make us dizzy and that might hint at some fundamental physical difference.

Are their any other, maybe unique, insights from special or general relativity regarding these two "types" of motion? For example the "equivalence principle" would seem to break down with rotational motion...since I think we'd sure know the difference versus gravitational effects.

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Jonathan Scott
Gold Member
I've always found rotational motion a little weird...

The "odd" result is that a while a fixed linear force causes steady acceleration and an ever increasing speed with a fixed direction a fixed rotational force causes steady acceleration via a steady change in direction while speed remains constant. And that's because acceleration and velocity vectors are coincident in linear motion and offset 90 degrees with uniform rotational motion.

But as one "silly example" of how they may be different, linear acceleration doesn't make us dizzy and that might hint at some fundamental physical difference.

Are their any other, maybe unique, insights from special or general relativity regarding these two "types" of motion? For example the "equivalence principle" would seem to break down with rotational motion...since I think we'd sure know the difference versus gravitational effects.
The gravitational effects of a moving or rotating body include "gravitomagnetism", which is equivalent to a rotating frame of reference and "frame-dragging" effects. "Gravitomagnetism" is related to the ordinary gravitational acceleration field in the same way that magnetism is related to electrostatic fields. In gravity, this is normally an extremely tiny effect, but Gravity Probe B has been attempting to measure it experimentally.

Here's another insight from Fredrik in another thread:

So why did I say "if the acceleration is linear..."? Because there are situations where it just isn't possible for each microscopic piece to restore itself to its original length in co-moving inertial frames. The simplest example is a rotating disc. When you give a wheel a spin, the material will be forcefully stretched everywhere along the circumference by a factor that exactly compensates for the Lorentz contraction. So in this case we are performing additional work, not to cause the Lorentz contraction but to make sure that lengths remain the same when they do get Lorentz contracted.

I am unsure of any possible differences between rotational and linear frame dragging, but they might affect light somewhat differently:

(http://en.wikipedia.org/wiki/Frame_dragging)

Rotational frame-dragging (the Lense-Thirring effect) appears in the general principle of relativity and similar theories in the vicinity of rotating massive objects. Under the Lense-Thirring effect, the frame of reference in which a clock ticks the fastest is one which is rotating around the object as viewed by a distant observer. This also means that light traveling in the direction of rotation of the object will move around the object faster than light moving against the rotation as seen by a distant observer. It is now the best-known effect, partly thanks to the Gravity Probe B experiment.

Linear frame dragging is the similarly inevitable result of the general principle of relativity, applied to linear momentum. Although it arguably has equal theoretical legitimacy to the "rotational" effect, the difficulty of obtaining an experimental verification of the effect means that it receives much less discussion and is often omitted from articles on frame-dragging (but see Einstein, 1921).[4]

Another aspect of rotational versus linear motion in relativity I should have remembered and posted:
Brian Greene's explanation and diagrams showing how we move through spacetime at "c" has interesting visual distinctions between fixed velocity, and linear and rotational acceleration:
Constant velocity is straight line in space time, acceleration is a curve and rotational motion a fixed diameter corkscrew...but I can't see a fundamental insights this provides....maybe more imagination is required!!! It also provides a rather intuitive insight into why our universe is limited to "c".