How Is the Moment of Inertia Constant Determined Experimentally?

AI Thread Summary
The discussion focuses on experimentally determining the moment of inertia constant (k) for a hollow cylinder using a rolling object experiment. Participants analyze the relationship between the distance traveled by the object and the height from which it is rolled, aiming to derive k from the slope of a graph plotting x^2 against height (h). The equation x^2 = (4Hh)/(k+1) is restructured to fit the linear form y = mx + b, where the slope (M) corresponds to a specific value derived from experimental data. The challenge lies in correctly identifying the slope and its relation to the theoretical value of k, which is expected to be 1 for a hollow cylinder. Overall, the thread emphasizes the importance of graphing and understanding the relationship between variables to solve for k experimentally.
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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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