Measuring distance of rotating object

[Chynkinese]

Please ignore the periods in the diagram as it won't allow me to properly draw it otherwise.

I have an object, attached to a string, rotating uniformly in a circle but at an angle to the horizontal plane. It is going at 80RPM (so relatively slow). How would one go about measuring the length from stationary point o to moving object a? the length can range anywhere from 40cm to 70cm and the accuracy for the measurement should IDEALLY +/- 0.5cm (doesn't mean it has to since real life is never ideal).

ie......o
....../
....../
....../
...../
...a

Nothing can be attached to "a" unless it is extremely light (such as reflective tape for a laser or something).

I have a very simple idea but the accuracy is easily +/- 1cm to 2cm or so. It's a simply ruler with a pointer attached and I slide it as close as possible. And I do the same for the vertical (either that or I measure the angle, whichever is more accurate). It goes something like this:

ie...___Ruler___o
...|.../
...|.../
...|.../
...V./
...a

I thought about using a laser somehow but I can't seem to find any equipment suitable for this.

 

[minger]

Is the distance your measuring from the axis of rotation or arbitrary? How quickly do you need the data (refresh rate)?

Is the rotation steady?

What type of equipment do you have at your disposal?

 

[Chynkinese]

I'm measuring from the axis of rotation (axis goes vertically through point "o").

Rotation is assumed to be steady; it is done by the motor taken from power drill and fed by a lab DC power supply which is kept at a constant amperage and voltage.

I have access to me equipment that is usually available in a well equipped lab. As well, I am free to order any other necessary parts. Granted, I'm not ordering thousands of dollars worth just to test a theory.

 

[minger]

Well, if you're measuring from the axis of rotation, then isn't the distance to the object simply the distance of the string that you used to connect it?

 

[Chynkinese]

The problem is the string elongates during rotation and we need to know by how much.

 

[RTW69]

Can you project the shadow of the moving object onto a white background. Mark the location and measure the distance to the piviot with a ruler. The light would need to be in the plane of the rotating object.

 

[minger]

If the rotation is steady, then a hand calculation would probably get you just as close as any measurement. Take your rotating velocity and mass and find the tension that is generated in the string. Find the stress->strain and then elongation.

 

[Chynkinese]

Can you project the shadow of the moving object onto a white background. Mark the location and measure the distance to the piviot with a ruler. The light would need to be in the plane of the rotating object.

That's an idea...I could give that a try but I don't know how accurate it'd be.

If the rotation is steady, then a hand calculation would probably get you just as close as any measurement. Take your rotating velocity and mass and find the tension that is generated in the string. Find the stress->strain and then elongation.

I thought about that. But the stress->strain requires Youngs Modulus does it not? I don't think it'd be possible to find the modulus for the strings I'll be using. :S

 

[minger]

I thought about that. But the stress->strain requires Youngs Modulus does it not? I don't think it'd be possible to find the modulus for the strings I'll be using. :S

Then do an experiment. Hang a weight from the string and measure the deflection. Boom, Young's modulus (or at least a very good number for you to use).