Experiment: Centrifugal Acceleration

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Centrifugal acceleration
Experiment Centrifugal acceleration
Category Mechanics
Used sensors Acceleration (without g), Gyroscope


The experiment "Centrifugal acceleration" is a very efficient and simple way to demonstrate the relation of centrifugal acceleration a and angular velocity ω. Both can be measured directly with the accelerometer and the gyroscope, so at a fixed radius r, we can easily measure the quadratic function a = r·ω².

This can be done with any means of rotating the phone fast and safely. Some suggestions would be a salad spinner or a (small) carrousel. You need to be able to control the angular velocity, so you can measure a as a function of ω for wide ranges of ω.

Requirements

  • A means of rotating your phone "safely" and at arbitrary angular velocities, like a salad spinner or a small carrousel.
  • As the phone usually is inaccessible in a moving setup, you may want to use the remote control for this experiment. So a second device for the remote interface is usually required as well. Alternatively, you can do a timed experiment and try to vary the angular velocity in the pre-set time.

Setup

Make sure that your phone is attached to or placed in your rotating device safely and make sure that the radius is constant. For example, in a salad spinner you should add some soft filling material (like cloth) to protect your phone and fix it at the outer part of the spinner. Rotating your phone at a string is unsuitable as the radius changes with the angular velocity when the angle of the string changes.

You should vary the angular velocity (rotation speed) evenly from zero to a "reasonable" maximum speed. If you are using the remote interface, you can comfortably see gaps in your plot and control the angular velocity to fill them.

A good way to verify the quadratic relation, you can check that the plot of a over ω² gives a straight line.

Analysis

In this case phyphox does not need to do that much. The data of both sensors is averaged over 0.5 seconds to avoid short acceleration peaks due to a bumpy rotation and to increase the precision. Besides that, phyphox only needs to calculate the absolute of each sensor as sqrt(x²+y²+z²) and plot them.

Problems and resolutions

  • I canot measure values above xxx. The limit of the sensors may vary a lot across different devices. Some phones cannot measure acceleration above 30m/s², while others can comfortably reach 80m/s². Similar variations apply to the gyroscope.
  • At some point the plot bends unexpectedly. As the experiment is not exactly in the range for which the sensors are typically calibrated, you might have reached a point at which your sensors react no longer linearly. You can check this by repeating the experiment with a different phone (ideally a different brand).

Demonstration video