Lab: Physical Pendulum

Lab: Physical Pendulum

Authors: Lab conducted by Mohammed Karim (author) and Richard.

Objective: Find the period of different physical pendulums with varying inertia.

Theory/Intro: We understand that varying inertia affect the angular acceleration. Now, with the new concepts of simple harmonic motion and oscillations, we will see how different inertia affect the oscillations involved in the period of a single oscillation.

Apparatus/Procedure:

              

Post pic of apparatus

               First, we were tasked with calculating the inertia for six different figure orientations as a prelab. (See Figure 20.1) When we had this value, we were able to continue with the procedure. Using the values of inertia, we found the period through a torque equation. We then compared this theoretical result with our experimental result. How we calculated our experimental period was by placing a photogate underneath the oscillating object, where it would track the oscillations by the tape that stuck out. The first object that we dealt with was a ring. This ring was treated as a point mass a distance r away from the radius. We solved the angular frequency and time by using the equation T= 2(pi)/omega where omega is sqroot(g/2r), and found a theoretical value of 1.06s. This was very close to our 1.07 value that we tested using the pendulum. Next, we had to calculate the expression for the period of each isosceles triangles oriented at the apex and midpoint of the base. (See Figure 20.2) As you can see, our theoretical values for time were 0.6503 and 0.5728 seconds, respectively. As for our experimental data, we received experimental values of 0.6574 and 0.5946 seconds.

Data Tables/Analysis:

Figure 20.1 - Inertia and Angular acceleration calculations for triangles (Circles not included as we did not use them for lab)

 
 

Figure 20.2- period calculations of the isosceles triangle

Experimental graph of Period of Isosceles around apex:

Experimental of Isosceles around Base

Conclusion: This lab was straightforward. We calculated the inertia, used that to find angular acceleration through a torque equation, found the value of angular frequency, and calculated the period. After finding a value, we compared our theoretical and experimental values and were extremely accurate. Practically to the nearest percent, if not closer. Our values would have been exact had our degree of oscillation been slightly less, due to us discounting sin (theta). Another uncertainty that could have affected our data would be the axis of tilt, certain shapes were not perfectly even and straight and as a result, oscillated at some angle. However, for the most part, it was really accurate and hard to complain about with such precision. Specifically, for the first part, we assumed that the ring is a point mass, a distance r away from the center, however, it is more of an inner outer radius. In order to get a much closer result, we would use (1/2M(Ro^2+Ri^2))