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I am currently taking an engineering course in statics and my teacher is insisting that an off-center force will NOT cause a free object to rotate. This goes completely against my intuition. Here is the problem we are working on:

Equilibrium problem where a rod is resting on a cylinder. There is an applied load to the cylinder which is offset from its center of mass. Only friction from the ground and the rod is keeping it in equilibrium

My intuition tells me that if there were no supports that the cylinder would rotate, and therefore the friction forces on the FBD would look like this:

Friction force on top of the cylinder going right, friction on bottom going left

However, my teacher says that it would not spin if there were no supports, and therefore the friction forces would look like this:

Both friction forces going to the left

I'm not really concerned about this particular problem, but the possibility that I have totally misunderstood this physics concept is very concerning to me. I have already looked on this forum for similar questions, and they all seem to say that a free object will rotate if a force is applied off-center to it. However, my statics professor is an very intelligent PhD, and I hesitate to disagree with her. Any help is very appreciated!

Qmechanic
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Peter Newell
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2 Answers2

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An off-center force is going to create a torque about the center of mass. If the object does not rotate, then there must be an opposing torque present.

In your problem, if you don't know the magnitude of F1 then the direction you assume may not matter much. If the magnitude comes out of later calculations, then the sign will tell you the "real" direction.

Now, if the off-center force creates a torque, does that mean the top of the cylinder would move backward in the absence of friction? No. It depends on the specific geometry. If the force is very near the center of mass, then the translation of the cylinder is much larger than the rotation, and the top of the cylinder will move to the right. If the force were near the bottom, then the rotation will be greater, and the top of the cylinder might move to the left.

There is a standard physics problem to determine the specific distance from the center to strike a ball such that zero frictional force is required for it to roll without slipping. Forces applied closer or farther from the center will cause frictional loads in opposite directions.

BowlOfRed
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"She told me that a space ship firing a thruster off-center would only translate, and not rotate. Are you saying she is wrong about this?"

Either you and your professor are still misunderstanding each other, or she is wrong which admittedly seems unlikely. What she is asserting is demonstrably false. Ask her why you cannot balance a horizontal pencil by the tip, because according to her, you should be able to. An off-center force acting on an a free body in space is equivalent to the ordinary experience of trying to balance an object on your fingertip against gravity when you don't place your finger under the center of mass. It will rotate (and fall). Inertial mass is equivalent to gravitational mass.

Tom B.
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