Centripetal Acceleration lab question

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SUMMARY

The discussion centers on determining the nature of centripetal acceleration in a lab report involving a rotating steel beam. The participant calculated an average centripetal acceleration of 4.85 rad/s² using the equation (ω²)(r) = ac, where ω is the angular velocity. The conversation highlights the importance of analyzing both x and y accelerations, which are expected to vary sinusoidally in circular motion, while their combined magnitude may remain constant. The accuracy of measurements and the relationship between velocity and acceleration are crucial for concluding whether the acceleration is constant, zero, or changing over time.

PREREQUISITES
  • Understanding of centripetal acceleration and its formula (ac = ω²r)
  • Familiarity with kinematic equations for circular motion
  • Experience with data analysis software for plotting and analyzing motion
  • Knowledge of measuring techniques for velocity and acceleration
NEXT STEPS
  • Research the principles of circular motion and centripetal acceleration
  • Learn how to analyze motion data using software like Logger Pro or MATLAB
  • Study the effects of measurement accuracy on experimental results
  • Explore sinusoidal functions and their application in analyzing circular motion
USEFUL FOR

Students conducting physics experiments, educators teaching concepts of circular motion, and anyone interested in the practical applications of centripetal acceleration in lab settings.

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1. This is more of a general question about a lab report I'm doing:
The purpose of this lab is to find if the acceleration of a person sitting on the end of a steel beam is moving at a constant acceleration, if they aren’t accelerating, or if acceleration changes with time.

I have all my data, equations, and final numbers I just can't tell what the centripetal acceleration is doing. Does it stay constant? or does it change with time?

Homework Equations


(ὠ^2)(r) = ac

The Attempt at a Solution


Here is my prediction:
(4.2^2)(.24m) = 4.21 rad/s^2 = ac
The actual fit number I came up with is 4.85 rad/s^2 and this was the average of a chart of average accelerations found from recorded different x and y values as a platform rotated around. I just can't tell if it is constant, changing with time, or 0.

Thanks for the help.
 
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It is very difficult to tell what the problem is. Was the person in circular motion?
How did you average the x and y accelerations? How were they measured?
For circular motion, I would expect the x and y accelerations to vary sinusoidally while their combined magnitude would be constant.
 
There is an amuesment park ride where people sit on the end of a rotating steel beam. For my lab we took a video of a beam rotating from its center. The camera was placed above the center facing down. After this was done it was brought into a computer program to be analyzed. We plotted points at the tip of the rotating beam as it went around. This gave us x and y and the t at which the occurred for every point (35 points plotted). From this we found Vx with: dx*dt and Vy with: dy*dt. Then we found the acceleration in the x direction with:dVx/dt and in the y direction with dVy/dt. Finally an average acceleration was found with SQRT((Ax^2)+(Ay^2)). From the average acceleration we are supposed to conclude if it was constant, 0, or changing. I'm having trouble figureing out which one it is. It is all dependent on the velocity. So as the velocity changes so does the acceleration?

I'm just worried because the last time we had a lab report (motion up and down an incline) I said the acceleration was changing and I lost a ton of points because it was constant.
 
So you have values of Ax, Ay and A = SQRT((Ax^2)+(Ay^2)) at various times?
What do the numbers look like? Have you got a graph of them versus time? I'm sure the Ax and Ay will vary, but the SQRT may well be constant to within the accuracy of measurement. Can you estimate the accuracy of your measurements of x, y and t? And deduce the accuracy of Ax, Ay and A from that? Only then can you say if they are constant to within the accuracy of measurement.
 

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