# A Reverse Startup Oscillation?

1. Jan 11, 2012

### Greg23

A "Reverse" Startup Oscillation?

I have a very flexible plastic ruler 61cm long, 5cm wide, and .2cm thick.

I hold it by one end, with the "width" vertical, and sight along the ruler "aiming" at any vertical edge (like a door jamb). When I quickly move the ruler to the left a couple of centimeters the free end first moves to the right, and Then follows to the left.

It seems as if the free end of the ruler is counter-rotated about an axis as the force acts to move the first portion of the ruler.

What is the explanation?

2. Jan 11, 2012

### ertansinan

Re: A "Reverse" Startup Oscillation?

Think about you are in the space with no gravity. When you pull the one end of ruller you will create torque on it. Because of this free end rotates with respect to center of mass.

Then you can think about the gravity. Gravity creates oscillation here?

Is it clear?

3. Jan 11, 2012

### Greg23

Re: A "Reverse" Startup Oscillation?

With the ruler's short edge vertical there will be several oscillations if I impart a large force. The same will be true in a near-zero environment. It is essentially a spring (although a poor one). Gravity is irrelevant.

I understand that as the near end pulls the center section forward it induces a far-section rotation about some axis, forcing the far end into an initial counter-rotation. What I am lacking is the formal descriptive framework of this action. This may fall into the realm of classical mechanics, but I'm hoping not.

What is the physics vocabulary that describes the action of the far end?

Last edited: Jan 11, 2012
4. Jan 11, 2012

### AlephZero

Re: A "Reverse" Startup Oscillation?

It's not impossible for this to happen, but it's rather hard to analyze your experiment because we don't really know how firmly you are gripping the ruler, so we don't know exactly what direction the end you are holding is pointing when you start it moving. The result would also depend on how fast you accelerate the ruler, relative to its natural frequency of vibration (flapping back and forth as it bends). It may also depend on the forces caused by the air resistance on the ruler. Too many unknowns ...

Clearly there is some minimum speed of movement below which this won't happen, because the forces on the ruler are too small to bend it much.

A simpler situation that is easy to analyze is if the ruler was laid flat on a slippery surface (e.g a block of ice) and you push one end of the ruler sideways without holding it.The force you apply at one end is equivalent to the same force in the middle, which pushes the ruler sideways, plus a couple, that rotates it. In this case, the rotation always "wins", and if you push to the left the far end of the ruler will start to move to the right, even through the ruler as a whole will moves to the left.

5. Jan 11, 2012

### Greg23

Re: A "Reverse" Startup Oscillation?

I'm afraid I'm not following the ice block scenario. If the ruler were "flat" and frictionless I would expect to see results consistent with a rigid mechanical system, pivoting around some point. In any case, a new system is being suggested, but I'd prefer to better define this one.

Imagine the ruler is held with the short edge vertical, and the long edge horizontal, in a vise that is rotated counterclockwise through 7° in 0.10 seconds, or 10° in 0.2 seconds (the details are moot). If you observe the far end you will see that its initial motion is clockwise, after which it stops and begins to rotate in the counterclockwise direction, (then oscillates, damps, and stops).

I'm not looking for a numerical answer, but rather a description of the bending, and by extension, the directions of the initial rotational forces along the sections of the "beam".

How does one explain the initial counter-rotation of the far end?
Is the description possible in Physics 101, or is it best described with classical mechanics?

Last edited: Jan 12, 2012