Is the Graph of Period vs. Radius in Circular Motion a Straight Line or a Curve?

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SUMMARY

The discussion centers on the relationship between the period (T) and radius (R) in uniform circular motion, specifically whether the graph of T vs. R is a straight line or a curve. The user conducted an experiment using a rubber stopper on a string and observed that while the log-Period vs. log-Radius graph was linear, the T vs. R graph appeared to suggest a curve. The user references the centripetal force and the relationship expressed by the equation ω²r, indicating that if this value is constant, the graph should theoretically be a straight line, aligning with previous lab experiences.

PREREQUISITES
  • Understanding of uniform circular motion principles
  • Familiarity with centripetal force concepts
  • Knowledge of logarithmic transformations in data analysis
  • Basic graphing skills for plotting experimental data
NEXT STEPS
  • Investigate the mathematical relationship between period and radius in circular motion
  • Learn about centripetal acceleration and its implications on motion
  • Explore the significance of linear vs. logarithmic graphs in physics experiments
  • Review experimental design techniques for measuring period and radius accurately
USEFUL FOR

Physics students, educators conducting circular motion experiments, and anyone interested in understanding the dynamics of period and radius relationships in uniform circular motion.

JohnSimpson
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Hi, I've recently done a lab where we are investigating circular motion. I've plotted a graph of Period vs. Radius, but I'm unable to tell if a straight line or some sort of curve would be better suited to the graph.

I've also plotted log-Period vs. log-Radius and it was a straight line which makes me think that the graph of T vs. R should be a curve, but when I look at my (possibly very flawed) data points a straight line seems better suited.

In short, my question is, is the graph of Period vs. Radius for uniform circular motion a straight line or a curve?

Edit: Forgot to mention this is the ol' rubber stopper on the end of a string and your swinging the whole thing around by holding onto a glass tube, with the weight being on the other end of the string)
 
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HINT: Given that the centripetal force is the same in all cases, what is the relationship between T and R?
 
I wish I knew.
 
What would you conclude if \omega^2 r is a constant?
 
We havn't been told any equations so I have no idea what that means
 
I'm fairly sure that if the experiment went according to theory, the graph would be a straight line.

I'm saying this because we did a lab like this, and all of our graphs were supposed to be straight lines to show a direct relationship.
 
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