(Special) relativity final question; gyroscope at relativistic velocities

• slaydez
In summary, the question asks for the time it takes for an indestructible gyroscope with negligible friction and rotating at 0.85 c to fall from a height of 15 meters in a vacuum, relative to an outside observer. The use of Lorentz equations is necessary, but the theory behind it is what stumps the person. While classical mechanics suggests it will fall like any other object, special relativity may affect its falling time due to time dilation. However, if there is no component of the rotational velocity in the direction of free fall, there will be no relativistic effect.
slaydez
This question on my final blew my mind and I have no clue where to even start: (verbatim, not exact wording and so 'theoretical' I almost posted it under relativity)

Given that an observer on Earth with acceleration due to gravity 9.8 m/s^2 has an indestructible frictionless gyroscope and a means by which to safely accelerate it to a rotational velocity of (some relativistic velocity, we'll say).85 c, how long will the gyroscope take to fall in a vacuum (I think the problem may have said neglecting air resistance) relative to the observer if dropped from a height of 15 meters? So to sum it up, g=9.8 m/s^2, and this 'indestructible' gyroscope with 'negligible friction' (Yes it's a crazy question) is dropped from a height of 15 meters through a vacuum while spinning at .85 c. How long will it take to fall relative to an outside observer?

Lorentz equations are necessary for sure, but it's not the calculations that really stumped me, it's the theory behind it. Part of me says (classically) it will fall just like anything else. If I'm not mistaken though special relativity applies to the gyroscope because it's moving uniformly. So would the gyroscope in effect fall "slower" to the observer due to time dilation occurring for an observer "on the gyroscope" such as an ant? As I said, I assumed it was a trick and wrote it off as simple mechanics. I don't even think it was a fair question to ask, mainly because it's slowly ruining my summer. Can anyone help me out?

hi!
under the assumption that there is no component of the rotational velocity which points in the direction of free fall there would not occur any relativistic effect, since such effects only occur in the direction of movement.

1. What is (Special) relativity and how does it affect a gyroscope at relativistic velocities?

(Special) relativity is a theory proposed by Albert Einstein that describes how objects with different velocities experience time and space differently. At relativistic velocities, the gyroscope's rotation will appear to slow down due to time dilation and its shape will appear distorted due to length contraction.

2. Can a gyroscope reach relativistic velocities?

Yes, it is possible for a gyroscope to reach relativistic velocities. However, it would require an immense amount of energy and is currently not feasible with our current technology.

3. How does the gyroscope's mass change at relativistic velocities?

According to the theory of relativity, an object's mass increases as its velocity approaches the speed of light. This means that the gyroscope's mass will increase as it reaches relativistic velocities.

4. Will the gyroscope's precession change at relativistic velocities?

Yes, the gyroscope's precession, or the rate at which it rotates, will change at relativistic velocities. This is due to the effects of time dilation and length contraction, which will cause the gyroscope's rotation to appear slower and its shape to appear distorted.

5. How does (Special) relativity affect the measurement of a gyroscope's angular momentum at relativistic velocities?

According to (Special) relativity, the conservation of angular momentum still holds true at relativistic velocities. However, the measurement of the gyroscope's angular momentum will be affected by the time dilation and length contraction effects, resulting in a different value compared to when the gyroscope is at rest.

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