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Acceleration is Proportional to the Square of the Velocity and Inversely Proportional to Radius

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Submitted by Rich on Mon, 06/26/2017 - 18:35

PocketLab in conjunction with a 33-45-78 RPM turntable is an ideal setup for studying centripetal acceleration.  There are two videos that can be found in the Videos page of this web site.  They show that (1)  keeping radius constant implies that centripetal acceleration is proportional to the square of the velocity, (2) keeping velocity constant while varying the radius implies that centripetal acceleration is inversely proportional to the radius.

The PocketLab is placed in its silicone protective case to provide greater friction so that it doesn't slide off the turntable.  Y is toward the center of the turntable, and X is in the direction of rotational motion of the turntable. Single-graph mode is used with acceleration selected to be graphed.

From the accel X data in the videos students can then use Excel, Google Sheets, or any other analysis software to make graphs of (1) accel X vs. velocity-squared, and (2) accel X vs. the reciprocal of the radius.  Both of the graphs should be pretty close to straight lines, giving support for the desired outcomes.




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