Rotation of rigid body in space

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Discussion Overview

The discussion centers around the dynamics of a rigid body in space, specifically focusing on the effects of applied forces and torques on the rotation and translation of the center of gravity (cg). Participants explore the relationship between torque, rotational acceleration, and the motion of the center of mass in response to forces applied at various points on the body.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant proposes that applying a force perpendicular to a line through the center of gravity at a distance L produces a torque that results in rotation without translating the center of gravity.
  • Another participant challenges this view, asserting that any force applied to the body will accelerate the center of mass, regardless of its position.
  • A follow-up question seeks clarification on whether forces can be summed as if applied to the center of mass, indicating an interest in understanding the principles of force and motion.
  • A participant confirms that in the equation ƩF = ma, the acceleration a refers to the acceleration of the center of mass.

Areas of Agreement / Disagreement

Participants express disagreement regarding the initial claim about the effects of forces on the center of gravity. There is no consensus on the relationship between torque, rotation, and translation of the center of mass.

Contextual Notes

The discussion involves assumptions about the application of forces and the resulting motion of the center of mass, which may depend on the specific conditions of the scenario being considered.

DgN
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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
 
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DgN said:
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.
 
Doc Al said:
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?
 
DgN said:
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.
 

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