For this experiment we used the laptops with LoggerPro, accelerometer sensors, and stop watches.
As seen in the above picture, the accelerometer sensor was mounted to the edge of a flat, spinning table and once spinning would give us an angular acceleration on LoggerPro. Next, with the use of stop watches, and our eyes, we measured how long it would take for the sensor to make an x number of full rotations, cycles. We then divided the time by the rotations to get a semi-accurate period,
T = (time)/(# of cycles)
and by using the period we can calculate the angular velocity,
w = (2pi)/T,
where w is the angular velocity.
We repeated this process a total of five times to get different accelerations and periods. Using the calculated and measured data from the five trials we made a linear graph represented by
y = mx => a = r(w^2)
where a, angular acceleration, is the y-axis, w^2, angular velocity squared, is the x-axis, and r, the radius, is the slope of the line.
By analyzing the a vs w^2 graph we see that the calculated radius is about 0.150 meters and we know that our actual radius is 0.180 meters. There is of course some human error in the measurements but we were able to see a relation between angular acceleration, radius, and angular velocity.
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