# Pendulum with a bob that changes its center of mass

1. Dec 2, 2014

### Walk Don't Sit

Hello all, this is my first post here. I will try to phrase it as best I can, my physics background is weak, so please be patient, and thanks in advance for your help! I tried researching simple pendulums but couldn't quite find an answer.

Suppose a person is suspended, prone, from a pendulum. They are released from some height, like a typical pendulum scenario. However, during flight they flex their trunk to their right (think trying to bring right shoulders to right hips) with arms and legs extended. My thought is that this would cause their flight path to change because their center of mass was moved outside of the original path.

Essentially, I'm asking what might happen if you had a simple pendulum but with a bob that could alter its center of mass position-- not vertically like a trapeze artist-- but in a medial-lateral direction.

Thanks!

2. Dec 2, 2014

### Danger

That's the same principle by which one "pumps" a playground swing in order to achieve more height. Whichever way the centre of mass shifts is the direction in which the path will be deflected and/or amplified.

3. Dec 2, 2014

### Walk Don't Sit

Thanks for your response. Do you think the COM change would be significant in changing the direction- or the momentum of the muscular contraction?

4. Dec 2, 2014

### Danger

The resultant motion would actually be very complex, because there would be twisting, altered return path, etc.. It's all really far beyond my ability to comment further. Someone else should be able to help you shortly.

5. Dec 3, 2014

### jbriggs444

To a first order approximation, the right-left motion of a pendulum will be independent of any pre-existing forward-back motion. Both are simple harmonic motion with identical frequencies. If you super-impose two such motions, you will typically get an elliptical path. If the motions combine just right you can get circular motion or straight-line motion on a new path.

As has been pointed out in other recent threads on playground swing pumping, you cannot directly change the position of your COM by contorting your body. Doing so would violate conservation of momentum. What you can do is to change the position of the chains on the swing or (in this case) the shaft of the pendulum relative to your center of mass. If you flex your body rightward (right shoulders toward right hips) then your trunk and the pendulum support moves leftward. This results in a rightward net force which will, over time, deflect your COM rightward.

The shift in COM relative to the support point also results in a net torque. Having moved the bulk of your mass to the right of the support point, the right half of your body will begin to rotate downward. If nothing further is done, this rotation will tend to return the COM back to a spot directly under the support point. Managing this sort of rotation is a key to pumping a children's swing at low amplitude.

6. Dec 3, 2014

### Walk Don't Sit

"you cannot directly change the position of your COM by contorting your body. Doing so would violate conservation of momentum"

I thought I could, for example, raise my arms overhead and that would raise my center of mass. Or, starting in anatomical position, raise my right arm and that would move my center of mass towards the right.

You're saying I can change my body position relative to the COM but not the COM, right?

7. Dec 3, 2014

### Staff: Mentor

Right, with the small edit that I made above in the interests of precision.

8. Dec 3, 2014

### Walk Don't Sit

Thanks for your answers! Not to tax interest in the subject but if I may ask...

I think I'm still missing understanding something about how the interaction of forces is different in the trapeze versus if I made similar movements standing on firm ground.

If I'm standing and lean my trunk to the right I would expect my COM to shift to the right, or if I raise my arms overhead for it to shift higher. I suspect the ground provides a counter force but is there a simple way to conceptualize how/why the COM is moving in that case?

9. Dec 3, 2014

### jbriggs444

The difference is what you are pushing against. If you are standing on the ground you can push on the ground. The ground is quite massive, so it will sit still while you push on it. By Newton's third law, the ground pushes back on you and you move. You move and the earth stays in place (more or less).

If you are hanging on a pendulum you can push on the shaft. If you are hanging on a swing, you can push on the seat/chains. But those are not very massive. They will not sit there while you push on them. They will move away before you can push very long and hard. So you will stay in place (more or less) while the pendulum shaft or swing chains move away.

Of course, having the pendulum shaft or swing chains at an angle will result in a restoring force. So your center of mass will end up moving. Just not right away.