# Is rotational motion relative, as is linear motion?

In special relativity only relative velocity is what matters. A rocket and the universe can be in relative linear motion. In the rocket the universe is in motion. The universe got this motion when it fell freely in the gravity field present for the observer in the rocket. For the observer, the objects of the universe have all obtained kinetic energy. If one of these objects hits an object at rest in the frame of the rocket, the object will receive kinetic energy and momentum. In the frame of the universe, the object will give an object in the universe energy and momentum.

Can the same be said for rotational motion? Is this motïon relative too? For an observer on a rotating object the universe rotates and for an observer in the universe the object rotates. The motion is an accelerated motion but at any instant there is a relative linear motion. An instantaneous linear relative motion.

So can we say the universe rotates around the Earth?

• – rob
Commented Jul 16, 2021 at 11:29

No. Rotation is non-inertial motion, so it is invariant not relative. It can be detected locally using a gyroscope, regardless of the relative motion of any other object. The Earth is rotating at a rate of $$2\pi$$ radians per sidereal day, without reference to the rest of the universe.

• Fun fact: comments from deleted users can't be moved to chat, so the only way to clean up this comment thread was to put it in the dustbin. Bummer.
– rob
Commented Jul 17, 2021 at 14:24
• @rob no worries, that is probably where it belonged anyway
– Dale
Commented Jul 17, 2021 at 15:10

I have read that a good inertial guidance system can determine its rate of rotation by looking at the interference between two beams of light sent in opposite directions around a circular fiber optic multi-loop. This references nothing outside of the system (but it may be set to zero by looking at the direction to a distant star).

• The light, if the fiber rotates, can also be seen to cause interference because the light is framedragged by the matter rotating around it.
– user307025
Commented Jul 16, 2021 at 15:07

" For an observer on a rotating object the universe rotates and for an observer in the universe the object rotates "

The difference is that the observer on a rotating object can see an accelerometer that he is holding to show some reading. But the observer in the outside universe will see that the accelerometer he is holding will not show any reading. So, those 2 observers are not equivalent, unlike in the case of linear motion, where any experiment done by the 2 observers. moving with uniform velocity relative to each other will give the same results.

• You compare two different things. The observer in the univerde sees also a reading. If the metrr is on the rotating object. He thinks the reading is due to the rotation of the object. A person on the object thinks the rotation of the universe (wrt to him) is the cause.
– user307025
Commented Jul 16, 2021 at 19:45
• Why/how would the observer in the universe see a reading ? His accelerometer will NOT show any reading. Only the rotating person's accelerometer will show a reading Commented Jul 16, 2021 at 19:49
• Not his reader. But the experiment done is the one in thhe rotating frame where the accelerometer is rotating along. The observer holding one in outside the rotating object performs a different experiment.
– user307025
Commented Jul 16, 2021 at 19:53
• Yes, each guy checks the reading on his own accelerometer. One of them sees a reading whereas the other ones sees zero reading Commented Jul 16, 2021 at 20:19
• But then the experiments done are not the same. The experiments then are checking a meter in a force field and checking a meter in free space.
– user307025
Commented Jul 16, 2021 at 20:22

In one sense yes, you can consider accelerated motion to be relative if you wish. If you get into your car and accelerate down the road, you can decide that you are stationary and the Earth is accelerating away from you. However, if you adopt that viewpoint, then you will find it very difficult to formulate a consistent mathematical model to describe what is happening. You will find, for example, that the force required to make the Earth accelerate away from you doubles if you double the mass of the stationary car, even though the mass of the Earth is reduced as a consequence.

The same is true of rotational motion. You might take the view that if you apply a torque to spin a turntable, it is the universe that rotates while the turntable remains stationary. You will find it very difficult, however, to formulate a convincing rule to determine how the applied torque is linked to the rate of rotation of the universe. You will find that the torque you have to apply to make the universe rotate around the turntable is not in any way related to the mass of the universe, but is directly related to the moment of inertia of the stationary turntable. Provided you are happy to accept such an explanation, then you can consider rotational motion to be relative.

There is a way to know when we are not rotating, and without look at the distant stars.

Suppose a rocket above the atmosphere, with the engines turned on so that it can stay at the same altitude over the Earth equator. Besides staying at the same altitude, the rocket can also use jets to rotate around the Earth at any desired speed.

Inside the ship, the local aceleration can be measured by dropping objects for example. The crew knows that it is not rotating when that acceleration is a local maximum. That means: if the tangential velocity is increased, it comes closer and closer to orbital speed, when the acceleration is zero. Increasing above the orbital speed, the acceleration start to increase to the opposite direction, but has no more a local maximum. The acceleration increases boundless.

If they look at the Earth at the local maximum of acceleration, it is rotating with the period of one day. That way, they know that the Earth is rotating.