# The concept of rotational equilibrium

1. Apr 10, 2013

### hms.tech

Here is a text from my Physics Book :

The net external torque on the object about any axis must be zero for it to be in rotational equilibrium.

I divide the torques into two categories, anticlockwise and clockwise. (This approach works fine for 2-D objects but will it work for 3-D objects as well ?)

I think i found an error in my book or it might be possible that there is something wrong with my judgment. There was this quick quiz question and it asked whether the object is in rotational equilibrium.

I say no, it shouldn't and i can prove it :
Consider the black spot as the pivot and if i were to take moments about this point of the two forces, i would find that $F_{1}$ and $F_{2}$ each provide a clockwise torque !

Yes i agree that the net torque about their point of intersection will be zero but not about the black spot(which also lies in the object)

2. Apr 10, 2013

Hi hms.tech, did the question specify whether or not the point of intersection of the three force vectors was also the center of mass?

3. Apr 10, 2013

### hms.tech

Not at all

4. Apr 10, 2013

Then I'm inclined to agree with you!

If it was the center of mass, the object would be in rotational equilibrium. If you take your pivot axis at the black dot as you suggested, don't forget to add in the inertia force to produce a torque that counters the torque from the applied force and all is right in the world again :)

5. Apr 10, 2013

### Staff: Mentor

What book are you using? Are you saying that the text claimed that the pictured object was in rotational equilibrium?

6. Apr 10, 2013

### hms.tech

This book was recommended as a great book for introductory physics by ppl here on PF
Physics for Scientists & Engineers by Serway.

As mentioned in the first post, there was this quiz on page 349~350 which asked whether the given object is in equilibrium, i stumbled across it while reading the text.

The answer given at the back of the book says this :
The object is in torque equilibrium but not force equilibrium.

I am seriously confused, is that possible ?

7. Apr 10, 2013

### arildno

"The object is in torque equilibrium but not force equilibrium.

I am seriously confused, is that possible?"

Sure. Consider an object in free fall. It experiences no torque, but definitely a force.

8. Apr 10, 2013

### Staff: Mentor

Is it possible for an object to be in torque equilibrium but not force equilibrium? Only if the torque about the center of mass is zero. In which case the object will have a translational acceleration, but not a rotational acceleration about its center of mass. (Usually these issues are addressed in your next mechanics course. I doubt Serway covers these cases.)

I would say that the book is wrong about that question. (Unless they are talking about the line of action intersecting at the center of mass. But I don't think the book is covering such issues.)

9. Apr 10, 2013

### hms.tech

I think that even if all three forces were passing through the Center of mass, there MIGHT still be a net torque !
Let me prove it : https://www.physicsforums.com/attachment.php?attachmentid=57701

Consider this diagram in which the three forces are passing through the Center of mass (I am assuming this to prove my point). A point (black) is taken to be the pivot. Will there not be a net torque about this black spot ? (i think there will. )

Both $F_{1}$ and $F_{2}$ exert a clockwise torque ! ( i really cant see the possibility of an inertia force on the center of mass as suggested by cactusCookies; it does not make sense)

10. Apr 10, 2013

### Staff: Mentor

Is there a torque about the black spot? Sure. But be careful about what conclusions you draw from that, since the black spot is accelerating. It still turns out that there will be no rotational acceleration of the object.

One way of dealing with the fact that you are using an accelerating point as your pivot is by introducing inertial forces as cactusCookies stated. (The center of mass is a special point--it doesn't matter if it is accelerating or not.)

As I hinted, these more advanced issues are dealt with in your next mechanics course (e.g., Classical Mechanics).

Last edited: Apr 10, 2013