Near-C Speed Spinning Top: Immovable Object?

[nitsuj]

Idealizing material properties away (if it is possible for the "mechanics" of the question), would it be near impossible to push over / change orientation of a "top" spinning at near c speeds?

 

[Nugatory]

Just as with any other gyroscope, if you try to tip it in the east-west direction, the axis of rotation will rotate in the vertical north-south plane.

 

[nitsuj]

does that resistance go up the faster the top spins?

 

[Jonathan Scott]

The resistance to tipping is because the change in angular momentum produced by attempting to tip it is likely to be small compared with the existing angular momentum, so the relative change in the overall angular momentum direction is similarly small. So it's not that trying to tip it has no effect, but rather that the effect of applying the tipping torque is small compared with the existing angular momentum, and the larger the angular momentum, the less the effect for a given amount of torque.

 

[Nugatory]

does that resistance go up the faster the top spins?

Yes, just as does it does with a classical gyroscope. The relationship between the rotational velocity and the angular momentum differs from the classical relationship when relativistic effects are considered, but it's still angular momentum and its reaction to a tipping force is the same.

 

[nitsuj]

Not cool, but informative! thanks guys :)

I was "intuiting" that due to c there would mathematically be a point where there isn't "room left" in c to add more (kinetic?)energy to the object and in turn add more velocity. In the similar fashion to acceleration of an object in a straight line approaching c. Thought rotation could make an "immovable" stationary object. "direction of energy" seems to be pretty important here lol

Would mass of the rotating (oscillating) object have any impact on the emergent property? Oh...it is mass..is that right (the analogy) ?

 

[nitsuj]

The resistance to tipping is because the change in angular momentum produced by attempting to tip it is likely to be small compared with the existing angular momentum, so the relative change in the overall angular momentum direction is similarly small. So it's not that trying to tip it has no effect, but rather that the effect of applying the tipping torque is small compared with the existing angular momentum, and the larger the angular momentum, the less the effect for a given amount of torque.

Is that torque a decent analogy to "inertia", or more specifically have any simple math relation?

 

[Jonathan Scott]

Is that torque a decent analogy to "inertia", or more specifically have any simple math relation?

Torque is part of the Newtonian terminology for the mechanics of rotation, along with angular velocity, angular momentum and moment of inertia.

Torque relates to angular momentum in the same way that force relates to linear momentum. When you try to tilt a gyroscope, you are trying to rotate it about a horizontal axis. You can represent the angular momentum by an (axial) vector along its spin axis, vertically. When you try to tilt it, you are trying to add a small horizontal component to that spin axis, but in comparison with the initial spin that is tiny so it is difficult to make much of a difference. For a top or gyroscope being affected by gravity, once it is leaning there is then a torque due to gravity which continues to try to rotate it downwards, but as the resulting change in the spin axis is sideways it starts to turn in that direction, causing a steady precession.

 

[jartsa]

Idealizing material properties away (if it is possible for the "mechanics" of the question), would it be near impossible to push over / change orientation of a "top" spinning at near c speeds?

That top has a large rest mass, so it has a large rotational inertia, so it would change orientation quite slowly when pushed with non-huge force.

If you use a large force to force the top to change orientation quickly, then the top will slow down temporarily, so that speed stays below c.

 

[PeterDonis]

I was "intuiting" that due to c there would mathematically be a point where there isn't "room left" in c to add more (kinetic?)energy to the object and in turn add more velocity. In the similar fashion to acceleration of an object in a straight line approaching c.

This isn't quite correct even for linear motion. There is no limit to how much kinetic energy can be added to an object. As velocity approaches c, adding a given amount of kinetic energy equates to less and less velocity added, but you can always add more energy.

 

[jartsa]

That top has a large rest mass, so it has a large rotational inertia, so it would change orientation quite slowly when pushed with non-huge force.

If you use a large force to force the top to change orientation quickly, then the top will slow down temporarily, so that speed stays below c.

A little bit of clarification:

The large rest mass is caused by the fast rotation, fast rotation of large rest mass means large angular momentum, which means it's difficult to change the orientation. And the slowing down of rotation is the time dilation effect.

The rest mass of a top that rotates ridiculously fast is located mostly at the periphery of the top. Such top has about the same rotational inertia as a ring with same rest mass and same diameter.