How Is the Moment of Inertia Constant Determined Experimentally?

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SUMMARY

The discussion focuses on the experimental determination of the moment of inertia constant (k) for a hollow cylinder using a ramp setup. The relationship between the height of the ramp (h), the height from the table to the floor (H), and the distance traveled (x) is established through the equation x² = (4Hh)/(k+1). The participant derived a trendline equation, x² = 1.98h - 0.086, and is attempting to relate the slope of this trendline to the moment of inertia constant k, which is theoretically known to be 1 for a hollow cylinder.

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  • Understanding of moment of inertia and its significance in rotational dynamics
  • Familiarity with linear regression and trendline analysis
  • Knowledge of basic physics concepts related to energy and motion
  • Ability to manipulate and rearrange algebraic equations
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  • Study the derivation of moment of inertia for various shapes, focusing on hollow cylinders
  • Learn how to perform linear regression analysis using tools like Excel or Python's NumPy
  • Explore the implications of experimental errors in physics experiments and how to minimize them
  • Investigate the relationship between potential energy and kinetic energy in rolling motion
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Students in physics or engineering courses, educators teaching mechanics, and anyone interested in experimental physics and the principles of rotational motion.

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Homework Statement


For a little background, this lab was on energy of a rolling object. We rolled a hollow cylinder from the top of a ramp on a table and onto the floor. We are trying to experimentally derive the constant (k) found in the equation for moment of inertia.

Variables: h = height from top of ramp to table, H = height from table to floor, x = distance ball travels from end of ramp to its landing on floor

Make a graph of x^2 vs h. Add a trendline. Calculate k from the slope of the trendline as it corresponds to x^2 = (4Hh)/(k+1)

My trendline equation is x^2 = 1.98h - .086

Homework Equations



I = kmr^2
x^2 = (4Hh)/(k+1)
We know theoretically that k=1 for a hollow cylinder

The Attempt at a Solution


At first I thought the slope was k but that doesn't make sense because my expected k is 1.
I could just calculate k given my experimental measurements, but that's not what they're asking. I'm trying to relate the given equation to mx+b form but I'm drawing a blank. I don't know how to start.

Thanks!
 
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You have x2 = (4Hh)/(k+1) ⇒ x2 = (4H/(k+1)) h

this is in the form Y=MX+C, Y=x2 and X=h. What is M?
 

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