kinetic and potential energy question

[Tarinth]

So, in our campaign we have a metal called aetherium. It is inspired by the Rod of Immovability.

Just like the rod, we found a gigantic sphere of this metal in it's immobilized state. The DM ruled that the entire plane, which was a disc, moved through space facing forward and spinning, creating a circular trench around the plane as the immovable sphere resisted it.

When we turn it off, it is now free to interact with the plane as a normal object. Here's the question. How does it interact with the plane?
Does it:
A: do nothing and just sit there?
B: go spinning off like crazy as the spin off the plane transfers energy into it?
C: do something completely different?

Thanks in advance for your insight.

[Anymage]

Standing still in its own reference frame and having a constant speed in the plane's reference frame mean functionally the same thing.

And you can probably be safe treating a magically granted velocity that just got turned off the same as if there were a sudden meteor strike with that speed. If the metal object is slow but inexorable, stopping the magic would most likely make the object come to rest in a bit. If it's going about as fast as a boulder that had just rolled down a hill, you don't need too much dirt to stop that boulder.

[Rydiro]

So, in our campaign we have a metal called aetherium. It is inspired by the Rod of Immovability.

Just like the rod, we found a gigantic sphere of this metal in it's immobilized state. The DM ruled that the entire plane, which was a disc, moved through space facing forward and spinning, creating a circular trench around the plane as the immovable sphere resisted it.

When we turn it off, it is now free to interact with the plane as a normal object. Here's the question. How does it interact with the plane?
Does it:
A: do nothing and just sit there?
B: go spinning off like crazy as the spin off the plane transfers energy into it?
C: do something completely different?

Thanks in advance for your insight.

It has its fomer Inertia of trench digging, but now friction catches up to it. This would result in a halt, rather sooner than later. Depending on the trench/sphere etc.
So it gets to 'rest' on the rotating disc.

[halfeye]

So, in our campaign we have a metal called aetherium. It is inspired by the Rod of Immovability.

Just like the rod, we found a gigantic sphere of this metal in it's immobilized state. The DM ruled that the entire plane, which was a disc, moved through space facing forward and spinning, creating a circular trench around the plane as the immovable sphere resisted it.

When we turn it off, it is now free to interact with the plane as a normal object. Here's the question. How does it interact with the plane?
Does it:
A: do nothing and just sit there?
B: go spinning off like crazy as the spin off the plane transfers energy into it?
C: do something completely different?

Thanks in advance for your insight.

I'm a bit confused. If the object was originally stationary and the plane was moving toward it, then there ought to be a hole through the plane, not a trench? or is your DM's ruling saying that's what happened despite all the rest?

If your DM can rule that, I'd say they're good to rule the rest, and you'll just have to put up with it, because there's no guessing what that DM will come up with.

[Tarinth]

The DM says the sphere was in magical stasis independent of the plane. When released, there were various opinions on how it would reach equilibrium with the plane's rotational movement. Our DM argues that it would be the same as putting a marble on a spinning record.
While that may be the case, I'm not sure, it runs contrary to general D&D rules where things that teleport around tend to immediately establish equilibrium and not worry about the old star trek questions. When Kirk teleports down to a planet spinning through space, why isn't he smashed?

[gomipile]

The DM says the sphere was in magical stasis independent of the plane. When released, there were various opinions on how it would reach equilibrium with the plane's rotational movement. Our DM argues that it would be the same as putting a marble on a spinning record.
While that may be the case, I'm not sure, it runs contrary to general D&D rules where things that teleport around tend to immediately establish equilibrium and not worry about the old star trek questions. When Kirk teleports down to a planet spinning through space, why isn't he smashed?

I'd say your DM's answer feels better. How the effect of that looks depends entirely on specifics you haven't told us, though.

How far is the sphere from the center of the plane's rotation? How fast was the apparent difference in speed between the plane and the sphere before it was shut off?

If it's comfortable to stand at a point near the trench and doesn't feel like you're on the side of a steep hill or mountain, then there isn't much difference between your positions, in practice.

[El'the Ellie]

If I'm understanding it correctly it's like a lathe, with the sphere being the cutting head of the lathe, and the plane being the wood. From a 'godly' frame of reference, we see the sphere be stationary and the plane spin. An observer on the plane (who is rotating along with the plane) would see the sphere traveling along the plane, being 'pulled' by some invisible force. Once the sphere is made movable, it will start to gain kinetic energy as the sphere turns beneath it. Or more accurately, friction will pull it along with the plane.

If the speed of the rotation were very very high, or the friction very low, it could fling off the side. (More accurately, the friction on the plane wouldn't be strong enough to stop the sphere from travelling in a straight line) However, we know that's probably not the case, because you (and everything else in existence) is affected by the same rotation speed and hasn't been flung off. If the plane was like glass, it would be fair to say it's like dropping a marble on a spinning record. But the surface of the plane is full of dirt and rock and air and other sticky things. It's more accurate to say that it's like placing a marble on a record lathered with peanut butter.

It certainly won't fly off in a direction, as that sphere has no kinetic energy right now: it's gradually given some by the friction of the spinning plane, but that just gets it up to speed with everything else on the plane. It would probably come to a slow 'stop' from an observer's perspective. In the 'godly' perspective, it is just going from a stopped position to slowly gaining speed in the opposite direction.

The plane would probably gain a very slight bit of speed, since it no longer has a 'brake' digging into it.

Side note: you can use the sphere in it's immovable state to help you find the center of the plane. As you travel away from the center, the sphere will appear to travel more quickly. As you travel towards the center, the sphere will appear to slow down. It 'travels' the circumference of a sphere equal to 2*pi*radius every time the plane rotates once. Since the speed of the plane rotating is (presumably) constant, the sphere will travel more quickly if the radius is 1,000 miles as opposed to say, 100 feet.