Role of Center of Mass in a spinning body without gravity

[blaisem]

Hi, I'm having a discussion with someone on the plausibility of the physics in a science fiction movie (I know, very efficient use of time!). There's a scene with a space station shaped like a ring. It has a center body that is attached radially to one edge of the ring. This space station is orbiting a planet. On the edge of this ring an explosion occurs out of a circular aperture, destroying that section of the ring, that sets the space station spinning at 68 radians per minute. Here is a picture of the clockwise spinning station just after the explosion.

His argument is the spin of the space station should have a natural wobble induced because its center of mass is offset after the explosion.

My argument is that without a net vertical component in the initial explosion, a force parallel to the spin vector, no wobble should be appreciably observed no matter where the center of mass is, particularly in such low gravity.

My background is limited, though. Any insight? I'd post the movie name for further reference, but I don't want to write any spoilers. I guess the underlying question is what role the center of mass plays in the spin resulting from a force acting tangentially on a ring-shaped mass orbiting a planet. Whether center of mass is even relevant to a spinning body in outer space.

Thank you for any information!

 

[Noctisdark]

If I understood why you mean, the center of the spaceship has gone out of the ring after the explosion then consider the angular momentum L = I*ω , which is a conserved quantity (yet we ignored the force done by the explosion by the ship), after the explosion L is the same, but the moment of inertia I has become so small (because the mass become so small) rearraging the equation yields to ω = L/I is higher then initial angular velocity, now if we consider that the explosion has done some force on the ship, it could have increase/decrease the angular momentum or even keep it the same but accelerate the whole ship in another direction, good luck

 

[A.T.]

My argument is that without a net vertical component in the initial explosion, a force parallel to the spin vector, no wobble should be appreciably observed no matter where the center of mass is, particularly in such low gravity.

The station will spin around an axis through it's center of mass. If that axis doesn't pass through the docking door center, the door center will move in circles (wobble).

 

[blaisem]

Thank you for the quick replies

The station will spin around an axis through it's center of mass. If that axis doesn't pass through the docking door center, the door center will move in circles (wobble).

By docking door center you mean the center of the ring?

What is the mechanism by which a torque in the x,y plane can accelerate something in the z direction?

 

[A.T.]

By docking door center you mean the center of the ring?

Yes.

What is the mechanism by which a torque in the x,y plane can accelerate something in the z direction?

I don't understand your question, but the details of the acceleration phase are irrelevant here. Once the explosion is over, the center of mass will move inertially, and any rotation will be around an axis passing through it. That follows from linear momentum conservation.

 

[blaisem]

Once the explosion is over, the center of mass will move inertially, and any rotation will be around an axis passing through it. That follows from linear momentum conservation.

Ok. Do you happen to know a source i can read more about how conservation of momentum always leads to rotation around the center of mass? Thank you.

 

[jbriggs444]

Ok. Do you happen to know a source i can read more about how conservation of momentum always leads to rotation around the center of mass? Thank you.

If rotation were around a point other than the center of mass then the center of mass would rotate around that point. That means that the body's momentum would be varying in a circular pattern rather than staying constant. Conservation of momentum requires that the body's momentum be constant.

 

[blaisem]

If rotation were around a point other than the center of mass then the center of mass would rotate around that point. That means that the body's momentum would be varying in a circular pattern rather than staying constant. Conservation of momentum requires that the body's momentum be constant.

Thank you. So if the center of mass is not at the center of a rotating body, a wobble will be induced?

 

[A.T.]

So if the center of mass is not at the center of a rotating body, a wobble will be induced?

https://en.wikipedia.org/wiki/Rotating_unbalance