4-Oct-2016: Demonstration--Centripetal Force vs. Mass* Angular Velocity^2, Radius* Angular Velocity^2, or Angular Velocity^2

Apparatus: A big disk, some masses, a motor, and a force sensor,

Purpose: To determine the relationship between centripetal force and mass* angular velocity^2; centripetal force and radius* angular velocity^2; centripetal force and  angular velocity^2.

Model: F= mrw^2
F is the centripetal force, m is the mass of the mass, and w is the angular velocity of the mass or disk.

Process: Professor set up the apparatus. He puts the force sensor on the center of the disk and ties a mass on the force sensor by using a long string. On the bottom of the disk, a motor is connected on the center of the disk to make the disk rotate.

     Then, by changing the mass, the length of rope, or the angular speed, we collect some data: 
the mass m, the radius r, the time of the disk for ten round t, and the force f

    r                    m                    t                    w                    f
 0.205              0.2                15.7               4.002           0.6844
 0.295              0.2                15.39             4.083           1.13
 0.41                0.2                14.37             4.372           1.67
 0.58                0.2                14.33             4.385           2.35
 0.58                0.2                12.38             5.075           3.13
 0.58                0.2                12.47             4.665           3.83
 0.58                0.2                10.16             6.184           4.753
 0.58                0.1                10.58             5.939           2.16
 0.58                0.05              10.74             5.850           1.03

   Keeping the r be constant, we plug  f vs. mw^2   into the Logpro to get the graph. According to the model f = mrw^2, in the graph f vs. mw^2, the slope of the graph is the radius r. r= 0.6411m. The actual raduis r=0.56m. These datas are different, and the determent's error and the friction between the disk and the mass may cause this error.

  



    
    Keeping the m be constant, we plug  f vs. rw^2   into the Logpro to get the graph. According to the model   f = mrw^2, in the graph f vs. rw^2, the slope of the graph is the mass m. m= 0.2052kg. The actual rmass m=0.2kg. These two datas are very close that mean we are doing well at this group of data.  

    Keeping the mr be constant, we plug  f vs. w^2   into the Logpro to get the graph. According to the model   f = mrw^2, in the graph f vs. w^2, the slope of the graph is mass*radius mr. mr=0.129kg*m. The actual mass*radius mr=0.116kg*m. These two datas are close, but they are not close enough. The determent's error and the friction between the disk and the mass may cause this error. 

    The mass m has uncertainty 0.01 kg, the radius r has uncertainty 0.001, the time of the disk for ten round t has uncertainty 0.01, and the force f has uncertainty 0.001. They cause about 1% off for the calculation.