Will an off-center force cause an object to rotate if there is no resistance?

Question

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:

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:

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

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!

Is there more information available about the setting of the experiment? Is there a fixed axis? Is C the axis/center of gravity? Is the experiment static or dynamic? — m93a, Feb 21 '18 at 16:42
Thanks for responding. No there is not a fixed axis, yes C is implied to be the center of gravity, and this is a static equilibrium problem. — Peter Newell, Feb 21 '18 at 16:49
Not clear if this a static question or not? If it is, PhD drawing is obviously correct. Just take the lower contact point as the axis of rotation and balance $F_1$ torque against $P$. — npojo, Feb 21 '18 at 19:11
Answers have already been given to this question, as you are aware. It is pointless to repeat them here. Probably your professor does not disagree with them. Perhaps the difficulty is that you have misunderstood what he has said. — sammy gerbil, Feb 22 '18 at 13:08
-1 Not clear. Confusing : You state in the title "if there is no resistance" but in your question you include friction forces. Aren't they resistance? You also state this is a static equilibrium problem, so there is no translation or rotation ... Answers have already been given to this question (without resistance), as you are aware. It is pointless to repeat them here. Probably your professor does not disagree with them. Perhaps the difficulty is that you have misunderstood what she has said. — sammy gerbil, Feb 22 '18 at 18:08
@sammygerbil in order to draw a FBD, you obviously have to know how it would act if there was no resistance in order to replace that resistance with a friction force. — Peter Newell, Feb 22 '18 at 21:57

score 0 · Answer 1 · answered Feb 21 '18 at 17:16

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.

Thanks, that makes a lot more sense regarding this particular problem. However, what I still don't understand is that when I went to ask her about it, she claimed that there would be no rotation in a free body if there is nothing to rotate about. 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? — Peter Newell, Feb 21 '18 at 19:25
You could turn that around and ask how space ships do rotate. Yes, they use off-center thrusters that create a torque about the center of mass. Given a force and distance from center, you should be able to calculate the torque. Given more information about the body, you should be able to then calculate the angular acceleration. — BowlOfRed, Feb 21 '18 at 20:15

score -1 · Answer 2 · answered Feb 21 '18 at 20:07

-1

"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.

answered Feb 21 '18 at 20:07

Tom B.

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How is balancing a pencil related to pushing a ball between two surfaces? – m93a Feb 21 '18 at 21:44
@m93a It's not. OP said: "My intuition tells me that if there were no supports that the cylinder would rotate" and "my teacher says that it would not spin if there were no supports" and "she claimed that there would be no rotation in a free body if there is nothing to rotate about. 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?" and "I'm not really concerned about this particular problem" – Tom B. Feb 21 '18 at 21:55
But it is related to pushing an intertial ball, off-center, with no other forces acting on the ball. Replace ball with pencil. Same result, rotation and translation. The pencil makes it more intuitive, but doesn't change the principles. – Tom B. Feb 21 '18 at 22:06
Don't agree. The ball is stuck between two surfaces. If you put a pencil there instead (the pointy end up, preferably), tie a string slightly below the center of gravity, pull it to the right and then look at the graphite marks on the upper surface, you definitely wouldn't find them going to the left. This is (somewhat) consistent with what the teacher says. And this is as close as you can get with a pencil, then you have to use real physics. – m93a Feb 21 '18 at 22:24
@m93a, the OP is asking about a free body, and using the problem to illustrate. Unfortunately, the problem is more complex than needed for his main concern, which is: I thought a free body will rotate under the influence of a force directed off-center, but the teacher says no. It's the title question. You are addressing the problem in the illustration. I am addressing only a part of it. You are actually agreeing with me at (2.) in your answer. – Tom B. Feb 21 '18 at 22:32
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I would encourage Peter Newell to continue thought experiments with the problem in the illustration using different masses for the upper surface, and different, but symmetrical, distributions of mass, for the disk. And continue to be skeptical with respect to authority ;) – Tom B. Feb 21 '18 at 22:38
Yes, you're right, that's the title question, sorry. But if you read a bit further, you'll find that the actual problem he is describing is not at all related to dynamic rotation (although he thinks it is). In the comments he says it is a “static equilibrium problem”. And, regardless of the title, I think that we should stick to the exact problem and solve it for the friction forces. And in this regard, the teacher is right :) – m93a Feb 21 '18 at 22:40
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Fair enough. As long as he realizes that his intuition, that a force acting off-center on a free body causes rotation, is correct. – Tom B. Feb 21 '18 at 22:57
@TomB. Thanks for focusing on what I was trying ask. To clarify, she explicitly said that in order for something to rotate, you need a pair of forces, not just one. Therefore the pencil thing doesn't work because she would say that it is the combination of the weight of the pencil and the normal force from the table that creates a torque. Basically, you need a force and a fixed axis to create a toque, and the fixed axis requires a second force to fix it. I'm still not sure about it though... – Peter Newell Feb 22 '18 at 00:48
I think the distinction between statics and dynamics is the source of at least some of the confusion. In short, inertia provides the second force, IF things are free to move. More later. – Tom B. Feb 22 '18 at 01:13
@PeterNewell, do you understand why, for the statics problem with the constraints shown in the illustrated problem, that your teacher is correct? – Tom B. Feb 22 '18 at 21:04
@TomB. I believe I understand why the constraints are correct, but it has become obvious that her explanation was not. I also definitely did not misunderstand her, so this is very unsettling that this is what she taught in class. I am going to go ahead and resolve the question anyway though. Thanks for the help. – Peter Newell Feb 22 '18 at 22:02

Will an off-center force cause an object to rotate if there is no resistance?

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