Lab #8: Centripetal Acceleration vs. Angular Frequency

Centripetal Acceleration vs. Angular Frequency 

Samuel
Ellis
Mia
9-28-2016

Purpose: 

  To determine the relationship between acceleration and angular speed.

Theory:

Centripetal acceleration , a = r*w^2. Centripetal acceleration can be determine by the radius of disk and how fast is the disk rotating. When an object is on the rotating disk, there's will be a centripetal acceleration force point to the center of the circle and a tangential force point perpendicular to the centripetal force. Based on what we know about centripetal acceleration, we can find centripetal force acting on the object.

Procedure:

1. Place the accelerometer under on the disk and connect them to the wheel. Verify that accelerometer reads 0 in the x-direction.
2. Place wheels up against the bottom of the disk. On the top of the disk, place an object with know distance from center of disk. 

3. Connect force prob to the object. 

4. Tape a piece of paper on the edge of the disk. Measure scanner can scan it every time paper pass through.

5. Collect period and acceleration data for a variety of rotational speeds by varying the voltage from the power supply feeding the motor. 

List/Data

(1)

r = 20.5cm

6.4 v

200g

t = 16.5sec

(2)

r = 29.5cm

6.4v

200g 

t = 15.4sec

(3)

r = 41cm

6.4v

200g

t = 14.37sec

(4) 

r = 58cm

6.4v

200g

t = 14.33sec

(5)

r = 58cm

7.0v

200g

t = 12.38sec

(6)

r = 58cm

7.6v

200g

t = 11.16sec

(7) 

r = 58cm

7.3v

200g

t = 12.47sec

(8)

r = 58cm

7.3v

50g

t = 10.74sec

Graphs

(Above is the graph of r*w^2 vs. force graph. We used r*w^2 instead of m*r*w^2, so we can use the slope to determine the mass. The slope is 0.2028, which is close to the mass of the object 0.2 kg.)

(Above is the graph of w^2 vs. force graph. we used of w^2 instead of m* r*w^2 so that we can use slope to find mass times radius. The slope is 0.1267 which is close to real mass times radius, 0.116.)

Conclusion:

  Based on what we know about centripetal acceleration, we are able to use formula to find its radius, angular frequency and mass. By plotting those point into LoggerPro, and use linear fit to find its slope; which will give us the expected value for radius, angular frequency and mass. In this experiment, our expected value was indeed close to actual value, however, there are some error occur during experiment that cause data not exactly match with given value. First, in between wheels and the disk, where are several gap in between that might give inconsistent kinetic friction that cause disk move slower or faster. Also, data was given in 2 to 3 significant figure, which is not precise compare to data in LoggerPro(5 sig fig).