Angular Velocity of a Strap

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Submitting Assignment: Angular Velocity of a Strap

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A metal 'strap' rotates with fairly low friction on a plastic die.  Half-rotations are timed using the TIMER program and preliminary conclusions are drawn about the nature of the motion.  Additional analysis based on the data taken here is conducted in a later lab exercise.  Most students report time of completion around 1 hour, with reported times ranging from 15 minutes to 2 hours or in isolated cases more.

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Angular Velocity of Strap

NOTE:  If you don't have the metal strap, you can replace it with the straw you used in a previous experiment, with three large paper clips attached at each end.

The picture below shows a metal strap rotating on a plastic die ('die' being the singular of 'dice').  In this picture the strap is kept from sliding off the die by a bent-out paper clip which goes through a hole in the center of the strap and into a small hole drilled in the die.  However the paper clip actually adds to the friction of the system and we have found that the strap can easily be made to rotate on the die without the paper clip, and the hole in the die has therefore been eliminated. 

A flat ceramic magnet is placed at each end of the strap.

There is a piece of paper under the system.

Set up this system in a place where you can reach it with your computer's mouse.  You might want to tape the paper to the tabletop, but it probably won't move so this might not be necessary.

The experiment is fairly simple and can be run in just a few minutes.

Get the TIMER program running on your computer.

For each trial you will do the following:

• First mark the initial position of the strap by marking a straight line just below the strap, and parallel to it.
• Place the mouse cursor over the Click to Time Event button and lift the mouse straight up, so the cursor doesn't move.
• You will need one hand to hold the paper clip in place and prevent the strap from sliding off the die.  Use the hand that isn't holding the mouse.
• You will quickly nudge the strap with your mouse hand, hard enough that it does through at least a couple of revolutions before coming to rest, and you will at the same time click the mouse to begin timing.
• Every time the strap passes the line you drew to mark the initial position, you will click the mouse.  The strap will pass this line every 180 degrees of rotation, two times per complete revolution.
• You will also click the mouse at the instant the strap comes to rest.
• You will then make another line on your paper, parallel to the strap.  Along this line you will write down the time intervals indicated by the timer.

Practice until you become confident of your ability to accurately time these events.

Then replace the paper and conduct 8 trials.  Vary the nudges so that the strap completes between half a revolution and a complete revolution with the lightest nudges, and several revolutions with the hardest, with a good spread in between.  Use the same starting position for each trial.

At the end of the 8 trials the paper will contain all the information you need to report.  A similar paper is shown below, but to avoid clutter here only four trials are indicated.  For example, if the rotation here is clockwise, the upper line appears to have rotated through three 180 degree intervals in .71, .93 and 1.20 seconds, respectively, then to have rotated to within about 45 degrees of the starting position in the last 1.97 seconds (rotating clockwise, it would therefore have rotated about 135 degrees during that last 1.97 seconds).

Take the paper and do the following:

For each final position, use the line you drew to estimate in degrees the angle through which the strap rotated after the last time it passed the position of the initial line.  You should be able to estimate this angle, which will lie between 0 and 180 deg, to within 10 degrees or so.  As we will see, it would be pointless to measure the angles with any more accuracy than this.

Report your data in the following format: 

Report one line for each trial.  The line should contain your estimated angle followed by a comma, then the time intervals associated with the motion of the strap, each followed by a comma.

For example suppose I reported the following line:

110, .80, 1.11, 1.63, 2.41, 1.97

this would tell me that the strap rotated through the first 180 deg in .80 sec, took another 1.11 sec to rotate through the next 180 deg, then 1.63 sec to go through a third 180 deg angle, then 2.41 sec to go through a fourth 180 deg, then 1.97 sec to go through a final 110 deg before coming to rest.

I would then be able to say a lot about the motion of the ramp.  For example I could conclude from this data that the strap passed through 180 deg + 180 deg + 180 deg + 180 deg + 110 deg = 830 deg in (.80 + 1.11 + 1.63 + 2.41 + 1.97) sec = 7.92 sec.  I could figure out that angular positions of 180, 360, 540, 720 and 830 deg occurred at .80, 1.91, 3.54, 5.95 and 7.92 sec.  I could do a lot of analysis with this data.

You don't need to do a lot of analysis at this point.  First report the data.  Give your 8 lines of data in the specified format.

Beginning in the subsequent line give a short narrative description of what your data means and how it was collected.

Do you expect that the strap is speeding up or slowing down as it rotates, and how do your results support or fail to support this expectation?

Now figure out how far the strap moved and how long it took for each of your 8 trials.  Report your results in 8 lines, in the format of the example line

7.92, 830

with the time in seconds reported first, followed by a comma then the angle in degrees.

On the average, through how many degrees per second did the strap travel on your first trial?  Explain how you calculate this result and give the result in the box below:

On the average, through how many degrees per second did the strap travel on each of your 8 trials?  Report as 8 numbers, one in each line

Your instructor is trying to gauge the typical time spent by students on these experiments.  Please answer the following question as accurately as you can, understanding that your answer will be used only for the stated purpose and has no bearing on your grades: 

• Approximately how long did it take you to complete this experiment?

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