# Rotational motion thought experiments

1. Apr 28, 2015

### pgardn

So say we have a stick in space with the CM in the middle and we apply two forces of equal magnitude and direction over the same time, one force at the CM, and the other at some distance away from the CM.

Ideas:
1. One would obtain just translational motion the other would have both translational and angular
2. One would not have angular momentum with respect to the path of the CM the other would, but both would have momentum in general.
3. One would have more work done on it in the same direction, the other would have work done in differing directions.
4. One would have only translational kinetic energy, one would have both translational and rotational K.
5. The acceleration of the CM would differ over this time.
6. I dont know quite how to think about the total distance over which the Force is applied for the Force at some distance away from the center of mass.

And its number 6 that got me wondering about all kinds of misconceptions. Any little piece of guidance that could make my ideas more accurate, because I break down at #6.

Last edited: Apr 28, 2015
2. Apr 28, 2015

### rumborak

I think if you want to keep applying the same off-center force, it will have to follow the spot that it is being applied on. Is that what you are asking?

Last edited: Apr 28, 2015
3. Apr 28, 2015

### pgardn

Im saying that it is given that the Force at some distance R away from the CM stays in the same direction and magnitude as the one at the CM

And this brings me to an error already. My #3 is incorrect. The work would be in differing directions throughout. (just reposted, this is wrong.)
I just started thinking about my initial conditions to compare, and then I realized I might not understand rotational motion very well.

Yes I am confused as to how these would compare. Now I am thinking about the path both would take and I am confused. Since the direction of the acceleration is changing.

Last edited: Apr 28, 2015
4. Apr 28, 2015

### pgardn

#3 is again wrong. The work would be in the same direction, but the r would be changing so the amount of work would be changing. And since I dont know how to figure out the direction, Im lost on the work done.

This is a tough one for me. So #3 and #6 have me confused.

5. Apr 28, 2015

### Staff: Mentor

If you apply the same force for the same time, the point of application for the one applied at some distance from the CM will move more. Thus, that force will do more work.

Obviously, if you keep pushing the thing will rotate and the distance from the CM will change. Instead of worrying about that complication, first treat the simpler case where the force is applied only for a short time.

6. Apr 28, 2015

### pgardn

Short time meaning just to start an impulse, or give no impulse...? Just a FBD at one moment? Enough time for distance to change in both directions or one direction?
How would the path of the CM look in 2-d though for off center torque?

Ok

1. Same as my original
2. Same as my original
3. Work done in both cases,
4. same as original
5. im now thinking the acceleration would be the same, but Im not sure why...
6. NA I guess.

I think I might be even more confused now thinking about Kinetic energy as well

7. Apr 28, 2015

### Staff: Mentor

Give it some impulse; you want the force to act for some time.

It would be useful to apply Newton's 2nd law for that moment.

Keep it simple. Keep the force acting in the same direction for the duration of the impulse.

The acceleration (and subsequent path) of the CM is determined by the net force acting on the object. It doesn't matter where that force is applied.

8. Apr 28, 2015