PHY11L - E203 MOMENT OF INERTIA

 

EXPERIMENT 203 : MOMENT OF INERTIA

 

DATA and OBSERVATIONS

TABLE 1.  Determination of Moment of Inertia of Disk and Ring (rotated about the center)
mass of disk, =          1475.7         grams mass of ring, =         1442.1           grams radius of disk,  =           11.5             cm inner radius of ring, =         5.37          cm outer radius of ring, =         6.375       cm			Actual value of moment of inertia of disk and ring                      =        147677.4319      g-cm2
friction mass =        15       grams                                    radius, =         1.25        cm
TRIAL	(mass of pan + mass added),	acceleration,		experimental value of moment of inertia,
1	25                    grams	0.258    cm/s2		148337.8755            gcm2
2	35                    grams	0.362    cm/s2		147994.3456            gcm2
3	45                    grams	0.460    cm/s2		149725.8832            gcm2
average				148686.0348            gcm2
% difference				0.68                 %

 

TABLE 2.  Determination of Moment of Inertia of Disk  (rotated about the center)
mass of disk, =        1475.7         grams radius of disk,  =          11.5           cm			Actual value of moment of inertia of disk  =        97580.6625          g-cm2
friction mass =         5          grams                                    radius, =         1.25         cm
TRIAL	(mass of pan + mass added),	acceleration,		experimental value of moment of inertia,
1	20                    grams	0.31    cm/s2		98759.07258            gcm2
2	30                    grams	0.47    cm/s2		97692.48670           gcm2
3	40                    grams	0.63    cm/s2		97182.53968            gcm2
average				97878.03299           gcm2
% difference				0.304                    %

 

                                                           

 

 

 

 

EXPERIMENT 203 : MOMENT OF INERTIA

 

 

 

 

 

TABLE 3.  Determination of Moment of Inertia of Ring  (rotated about the center)
mass of ring, =        1442.1           grams inner radius of ring, =         5.37       cm outer radius of ring, =        6.375     cm	Actual value of moment of inertia of ring           =         50096.7694            gcm2
experimental value of moment of inertia (by difference),                 =        50808.00181          gcm2
% difference	1.41              %

 

TABLE 4.  Determination of Moment of Inertia of Disk  (rotated about the diameter)
mass of disk, =       1475.7         grams radius of disk,  =          11.5            cm			Actual value of moment of inertia of disk  =         48790.33125             g-cm2
friction mass =        5          grams                                    radius , =         1.25            cm
TRIAL	(mass of pan + mass added),	acceleration,		experimental value of moment of inertia,
1	15                    grams	0.47    cm/s2		48846.24335               gcm2
2	25                    grams	0.78    cm/s2		49039.44314               gcm2
3	35                    grams	1.10    cm/s2		48666.90391               gcm2
average				48850.90391               gcm2
% difference				0.12                          %

 

                                                                                    

 

  GUIDE QUESTIONS

 

1.   Suppose the disk and the ring are of the same mass and radius. Which one has the greater moment of inertia? Explain why the moment of inertia of one is greater than the other.

 

 Even though a disc and a ring have equal masses and equal radii. The mass of the ring is distributed uniformly at a distance equal to the radius of the ring. In the case of the disc, however, while some mass lies on the circumference of the disc, most of the mass lies closer to the axis of rotation. Therefore, the moment of   inertia is greater for the ring than for the disc.

   

2.    Use equation 3 to derive the moment of inertia of a solid rod of mass M and length L if its axis is             perpendicular to the rod and through its center.

           I =∫r² dm

                I = ∫-_L/2r² M dr =  M  r³   L/2   = M  L³ - L³            dm =  M   dr

                                L             L    3    -L/2      3L   8    8                             L    

 

                        I _cm =   1 ML²

                                                  12

 

3.    In the figure below, the block on the inclined plane is moving up with a constant acceleration of 2.00m/s²

      Determine T1 and T2 and find the moment of inertia of the pulley.(Note: T1 and T2 are tensions on the two

      segments of the cord).

                                                             

                                                                                          10 kg = m1

20 kg = m2

 

 

 

30^o

 

            

 

 

 

 

 

 

 

 

 

 

 

 

 

ANALYSIS

   1.  Compare the experimental values of the moments of inertia of the disk and the ring. Why is the moment

        of inertia of one of them greater than the other?

              

     The moment of inertia of the disk is greater than that of the ring because in

    the computation of the moment of inertia of the disc, the radius of the disk is

    bigger than that of the total radius of the ring. Because of this, the moment

    of inertia of a disk is greater than the ring.

 

 2.  Why is the moment of inertia of the disk greater than that of the ring even though their masses are almost        

      the same?

 

       The moment of inertia of the disk is greater than that of the ring because the

      mass of the disk is uniformly distributed than that of the ring. In a ring, the

      weight is far from the center or the axis of rotation. This makes the moment of

      inertia of the disk greater than that of the ring.

 

   3.  Why is the moment of inertia of the disk greater when it is rotated about the center compared to when it is

        rotated about its diameter?

      

        The mass distributed when the disk is rotated at the center is far from the

        center of mass or the axis of rotation than when it is rotated about its

        diameter. Because of this, the moment of inertia when the inertia is rotated

        about a center is greater than when it is rotated in the diameter.

 

 

 

              

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CONCLUSION

 

     1.  Moment of inertia is the rotational analog of mass. If the mass of a particular rigid body is constant, why          

         is its moment of inertia not constant?                                                    

 

        The moment of inertia is not constant because of the external forces that act

        on the system. These external forces are the place of the axis of rotation, how

        far the mass units are from that axis and also the distribution of weight so

        even if the mass is constant, the moment of inertia changes significantly due

        to these forces.

 

 

 

     2.  What are the factors that affect the moment of inertia of a rigid body?

 

         There are many factors that affect the moment of inertia of a rigid body.

         The moment of inertia depends on where you place your axis of rotation, how

         far the mass units are from that axis, and on the density profile of the ma-

         rial. The further away a mass point, the larger its contribution to the mo- 

         ment of inertia. The more mass points you have, the more inertia you have.

                                                                                                                                                                    

 

     3.  What causes the rotational motion of a rigid body to change? How is the moment of inertia related to  

          angular acceleration?

          

          An object remains in a state of uniform rotational motion unless acted on

         by a net torque. Further, the angular acceleration of an object is propor-

         tional to the net torque acting on it, which is the analog of Newton's Second

         Law of motion. A net torque acting on an object causes a change in its

         rotational energy. Moment of inertia is related to angular acceleration

         from the formula of torque:

 

 

         Torque is the product of Moment of inertia and the angular acceleration.