Friday, November 2, 2012

Nonuniform Circular Motion

I was trying to create a non-uniform circular motion experiment this summer, but I was barking up the wrong tree.  I thought about swinging a ball in a circle at constant speed and have students derive the tension as a function of time or angle - measuring it with a force sensor - but you have to mess with the pivot point of the string (in a really interesting way) to make the ball move like that. Also - that's not non-uniform CM anyway! I then tried (at Physics Teacher Camp) to put a horizontal pole through the force sensor's mounting point and let a weight swing on a string - nonuniform CM was good, but the non-zero mass of the sensor ended up being a huge issue, and the tension was hardly ever parallel to the sensor's axis.

This week, I figured it out: the sensor is the ball. I attached a string to a rotary motion sensor (so that I could determine the angle and angular v as a function of time) and hung the force probe from it.

Puling it back and letting it swing, I got a good data set, even though I couldn't effectively zero the rotary motion sensor for some unknown reason.

Students then looked at the forces acting on the probe at some arbitrary angle and derived the tension as a function of angle and angular velocity.

To get the model to work without the rotary motion sensor being zeroed, I added an offset to the formula when I created a calculated column in Logger Pro. Once I did that, we could compare the graphs of actual tension (red) and predicted tension (pink):

There's an interesting time offset that I haven't explained yet: ideas?

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