# Experiment: Centrifugal Acceleration

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).