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?
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 said:does that resistance go up the faster the top spins?
Jonathan Scott said: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.
Torque is part of the Newtonian terminology for the mechanics of rotation, along with angular velocity, angular momentum and moment of inertia.nitsuj said:Is that torque a decent analogy to "inertia", or more specifically have any simple math relation?
nitsuj said: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?
nitsuj said: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.
jartsa said: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.