Purpose: The purpose of this lab is to figure out what is the relationship between centripetal acceleration and angular speed by looking at the acceleration vs angular speed graph that was represented by a spinning rotating disk with an accelerometer.
To set up this lab, Professor Wolf had it set up for us but it was a rotating disk attached to a spinning wheel that we could change how fast it went. There was also a photogate on the side. (It is a sensor where if there is something that comes in between it it takes the data.
BACKGROUND INFORMATION
An object that moves in a circle that is rotating, it is constantly changing velocity.
WHAT?! How does the velocity change?
It changes because the direction of the object is constantly changing which means that it is accelerating. This is centripetal acceleration and there is a centripetal force that pushes an object inward to the center.
The angular speed of an object is measured by taking radians divided by time (sec).
SIDE NOTE: linear velocity = radius * angular speed
The angular acceleration is measured by v^2/ r or (angular speed)^2 * r.
The lab itself was really fast so PROCEDURE
1. Since we wanted to find how much time it takes to make one rotation and the acceleration. We
started off with 4.4 volts and moved on to however many data points you want. We took data and it would give us time and how many rotations. We took a chunk of time vs a few rotations and just divided it in order to find the time for one rotation just to make sure if one rotation was off then we'd have an average of many.
The mass of the object was .1389 and you'd need this later to find the Force which is mv^2/r or in other words m * (angular velocity)^2 * r so I wrote down the data.
Professor Wolf read this out for us to write down so the whole class had the same data. We would subtract the time(final) - time(start) and divide it by however many rotations we decided to get the data points from. That would give us the time per rotation. We already have the acceleration due to logger pro for each data point.
Here we graphed our acceleration vs angular speed which gave us a value of close to 1 (.997) which means that there is a linear correlation between the two.
Conclusion:Errors in this lab could have occurred with friction of the rotations. There was definitely friction sometimes which meant that there could have been little errors in the reading. We reduced this error by taking many rotations and taking the average rotation for those. The point of this lab was to find the relationship between acceleration and linear speed and we did that by calculating the angular speed and graphed it with respect to time. We found out that the correlation between the two is proportional.
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