Lab 8 Demonstration Centripetal acceleration vs. angular frequency

Purpose: To determine the relationship between centripetal acceleration and angular speed.

In this experiment, we used a heavy rotating disk with an accelerometer attached to it. We used this device to measure how long it takes for the disk to make a certain number of rotations at different range of speeds.

Angular speed is the change in angle over time and is called omega . Centripetal acceleration is referred to the force acting on an object that's trajectory is a circle and is directed towards the center of its circular path.

To find angular speed we use the following formula :

 

 

Where t is the time for one rotation.

In this experiment the professor measured the acceleration and time of ten rotations of the disk and the whole class used the same data. We put the data into logger pro and inputted formulas into logger pro to calculate the omega and omega^2 values and got the following.

Then we made an acceleration vs. omega^2 graph and added a linear trendline.

The equation of the line given from logger pro is the same as :

Where ac is centripetal acceleration and w^2 is omega^2 and the slope of the trendline is r . This equation shows the relation ship between centripetal acceleration and angular speed to be as the angular speed becomes greater the centripetal acceleration will also become greater.

The graph shows that our radius is .1371 meters and when we measured the radius in class it turned out to be .139 meters. The radius in our graph was really close to the measured value in class. There could have been error as always because the equipment we were using was not the most expensive and was many years old . The accelerometer might not have been perfect at measuring the exact point of the rotation that is why we used ten rotations instead of timing just one.