Rolling Disc on an Inclined Plane | Engineering Mechanics Experiment #9

 

EXPERIMENT NO. 9

  OBJECTIVE:

 

To understand the relationships of mass moment of inertia, angular acceleration, and angular velocity of a disk rolling down an inclined plane.

 

APPARATUS:

 

Inclined Plane, Level Indicator, Height Adjuster, Rolling Disc.

                                       Figure 9.1: Rolling Disc on an Inclined Plane

 

THEORY:

Figure 9.2: Schematic Diagram on Rolling Disc on an Inclined Plane

 

A disc with mass m and radius R, rolls from rest at top position and takes time t (s), to reach bottom position. 

Let the linear velocity of the disc centre at the bottom position = v (m/s)  

Then, the angular velocity of the disc at this position = ω (rad/sec) = v/r (rad/sec)  

Average linear velocity = ½ v (m/s) = L/t (m/s)  

Where L is the linear distance travelled  

 

 

 PROCEDURE:

 

1.      The system is set up in horizontal position. To make sure the system is really in horizontal position, the bubble levels must be on center and ensure that the top surfaces of the two rails are at the same level. Wipe off any grease and dirt, which may be on the tops of rails. 

2.      Set one end of the two flanking rails of apparatus at a level above that of the    other end. Set a distance of L(m) along the length of the plane (m) and at height h=100mm between the extremities of the distance traversed by the centre of the disc. 

3.      Allow the spindle of the small disc assembly to rest on the two flanking rails and release it so that it starts rolling unaided down the incline, ensuring that the disc not rub against the rails during its motion. Note time t(sec) taken for the disc to traverse the distance L(m). 

4.      Carry out the procedures three times to get average time taken. 

5.      Repeat procedure for the other disc. 

 

 OBSERVATIONS: 

                          Table:9.1 

                          Table:9.2 

Table:9.3

CALCULATIONS:

     Large Disc:

•      Compare moment of inertia with respect to angle obtained analytically and experimentally.

•      Plot the graph between angle on x-axis and moment of inertia on y-axis obtained analytically and experimentally using Microsoft Excel.

     Small Disc:

•      Compare moment of inertia with respect to angle obtained analytically and experimentally.

•      Plot the graph between angle and moment of inertia obtained analytically and experimentally using Microsoft Excel.

CONCLUSION:

Discuss

•      The comparison between the results obtained analytically and experimentally.

•      The impact of angle on moment of inertia of small and large discs.

 

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