Rotation of rigid body in space

[DgN]

Hello,

I have been thinking about this for hours now but I can't seem to find a definitive answer so I hope you can help me. So here is my problem:

If you exert a force perpendicular to a line through the center of gravity at distance L you will produce a torque T, that torque will rotate the body around the center of gravity with a rotational acceleration w_dot = IT where I is the moment of inertia. Because this force is perpendicular to the leverage arm through the cg no force will be applied to the cg so we will have no translation of this point, only rotation. Am I right so far?

If my previous statements were correct I see a problem with my following resoning:
Imagine that the object in space is a long iron beam. If we apply a perpendicular force in one end it will start to rotate about cg. Now imagine that we move the applied force closer and closer to cg, the torque will become smaller but it will still produce only rotational movement as long as the force is perpendicular. As soon as the applied force hits straight on cg we will get zero torque and therefore no rotation but now the cg will translate according to F = ma. Is it really a sudden step between rotational movement and translational movement of the object or what have I missed? Will the cg start to translate even for perpendicular forces applied far from cg? Will objects in space always rotate about cg if torque is applied or can it rotate around other points?

I hope you can help, and I hope it is not something too simple that I have forgot so I don't have too feel stupid :P

Regards
Niclas

 

[Doc Al]

Because this force is perpendicular to the leverage arm through the cg no force will be applied to the cg so we will have no translation of this point, only rotation. Am I right so far?

No. A force exerted anywhere on the body will accelerate the center of mass.

 

[DgN]

No. A force exerted anywhere on the body will accelerate the center of mass.

Hmm, ok so you just sum all forces as if they were applied to the center of mass?

 

[Doc Al]

Hmm, ok so you just sum all forces as if they were applied to the center of mass?

Right. In ƩF = ma, a is the acceleration of the center of mass.

 

[PJC01]

Hello Niclas,

Thank you for reaching out with your question. Your understanding of rotational movement and torque is correct. When a force is applied perpendicular to a line through the center of gravity, it will produce a torque that will cause the rigid body to rotate around its center of gravity. This is because the force is not acting on the center of gravity, so it does not produce any translational movement.

As for your question about the sudden step between rotational and translational movement, it is important to remember that torque is dependent on the distance from the applied force to the center of gravity. As you move the applied force closer and closer to the center of gravity, the torque will decrease and eventually become zero when it is applied directly at the center of gravity. At this point, the rigid body will no longer rotate but will instead experience translational movement due to the force being applied directly to the center of gravity.

In general, objects in space will rotate about their center of gravity when torque is applied, but this is not always the case. If there are multiple forces acting on the object, it may rotate around a different point depending on the distribution of those forces. However, in most cases, the center of gravity is the point around which the object will rotate.

I hope this helps clarify your understanding. Keep asking questions and exploring these concepts - that's what science is all about! If you have any further questions, please don't hesitate to ask.

Best,