25-March- Centripetal acceleration vs angular frequency

Centripetal acceleration vs angular frequency

Purpose

To determine the relationship between centripetal acceleration and angular speed

Procedure

In this short lab we placed an accelerometer attached to a spinning disk. We then spun the diskl using different voltages and the sensor recorded how fast the disk was accelerating; the higher the voltage the higher the acceleration produced. Meanwhile, we timed a given number of rotations to figure out the period of rotation at every voltage. Using w=2pi/period we determined the angular speed at every single voltage. We then recorded the acceleration, period, and angular acceleration in a data table in LoggerPro and lastly we graphed it.

Recorded acceleration and angular speed

Graph: Acceleration vs Angular speed^2

Slope = radius = 0.13 m

Conclusion

After using a proportional fit on the graph above we see that the slope of the graph turns out to be the radius of the spinning disk. We compared the value obtained from the graph to the actual radius of the disk (obtained using a ruler) and it turned out to be the same 0.128 m or 13.8 cm. Thus we concluded that the experiment was successful as we proved that angular acceleration and angular velocity are related by the radius of the rotating object. 

a=rw^2