Rolling Motion, confusing with linearizing a graph?

AI Thread Summary
The discussion focuses on linearizing the equation a = ⅔g sin θ to facilitate graphing and analysis. By treating acceleration (a) as the y-variable and g sin θ as the x-variable, the relationship can be expressed as y = (2/3)x, indicating a slope of 2/3 and a y-intercept of 0. Participants clarify the process of linearization, noting that the resulting graph appears linear based on their data. The conversation emphasizes the importance of understanding how to relate the theoretical equation to a linear format for easier interpretation. Overall, the process of linearizing the equation simplifies the analysis of rolling motion.
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Homework Statement


Rolling Motion

Theoretically, a=⅔g sin θ suggests a nonlinear relation between a and θ. Since a linear graph is a very convenient method of testing theoretical equations, it is a good idea to first linearize a=⅔g sin θ. A simple way to do this is to assign a as the y-variable and (g sin θ) as the x-variable. If a=⅔g sin θ is linearized in this way, what are the expected values of the slope and y-intercept of the linear graph?

Plot a versus g sin θ. Perform a linear fit to the data, and determine the slope and the y-intercept. Compare the results with the expected values according to a=⅔g sin θ.

Homework Equations


a=⅔g sin θ

The Attempt at a Solution


I'm not exactly sure where to start! To be honest, I've never heard of 'linearizing' a graph before. Any insight into how to go about this would be greatly appreciated.

PS I made my graph from my data of acceleration and g sin θ, and it is indeed very linear. I'm just not sure how to relate it or how to find the 'expected' values?
 
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You're plotting ##a## versus ##gsin\theta##. So, think of ##a## as the "##y##" variable and ##gsin\theta## as the "##x##" variable. What would the equation ##a = \frac{2}{3} g sin\theta## look like using the symbols ##x## and ##y##?
 
y = 2/3 x ?
So 2/3 is the slope? And since there's no b, this means that y = 0?
 
Yes. Good. Note that y = (2/3) x is a linear equation. Thus, the word 'linearizing'.
 
Well... that was a lot easier than expected. Thanks for your time!
 
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