7-June-2017: Physical Pendulum Lab

Physical Pendulum Lab
May Soe Moe
Lab Partners: Steven Castro, Stephanie Flores
Date: 7-June-2017

Objective: To derive expressions for the period of various physical pendulums and to verify the predicted periods by experiment

Introduction:

We did the pre-lab questions for this lab, in which we derived expressions for the moment of inertia of the semicircle rotating around its midpoint, its rim, the moment of inertia of the isosceles triangle rotating around its apex, and its midpoint. Once we get our expressions for moment of inertia of theseshapes, we derived our angular frequencies by using torque equation: T=Iα. Then, we used our previous derived equation in class, which is α=ω^2θ. We first use the torque equation and find α and put it into "α=ω^2θ" form. Whatever constant in that form is our ω^2. And we will find its square root and put into period equation: T=2π/ω. Then, we will conduct an experiment of a semicircle rotating around its midpoint, and an isosceles triangle rotating around its apex, and figure out their period by using motion sensor and Logger Pro. After that, we will compare the theoretical value and our experimental value.

Experimental Procedure:

(1) We set up to conduct the experiment as below:

Semi-circle Oscillating around its Midpoint

Isosceles Triangle Oscillating around its Apex

PhotoGate will determine the period of the triangle as the triangle oscillates.

(2) We chose our physical pendulums to be a semicircle and an isosceles triangle.

(3) Semicircle rotates and oscillates around its midpoint, and the triangle rotates around its apex.

(4) We sticked a piece of paper at the bottom of the pendulums to make sure PhotoGate can sense their motions correctly.

(5) We connected PhotoGate to our laptop and Logger Pro.

(6) After all the set up, we gave a push to the pendulums to make them start oscillating, and started to collect data in Logger Pro.

Experimental Data and Measurements:

Measurements of the Semi-circle and Triangle Pendulums

Experimental value of Period of A Semi-circle rotating around its midpoint collected by the PhotoGate

Experimental value of Period of A Triangle rotating around its Apex collected by the PhotoGate

Theoretical Calculation:

Calculating the moment of inertia of a semi-circle rotating around its midpoint

Calculating Angular Frequency 

Calculating the Moment of Inertia of an Isosceles Triangle around its Apex

Calculating Angular Frequency of the Triangle around its Apex

Calculating the period by using the derivation from above

Comparing the results

Conclusion:
Theoretical calculation part of this lab was done by finding moment of inertia around the midpoint of the semi-circle, moment of inertia around the apex of the triangle, and by using torque equation to find the angular frequencies of the oscillating semi-circle, and the triangle. Once we have the angular frequencies of the pendulums, we could calculate the period. The experimental part was done by using PhotoGate to figure out pendulums' periods. Now, when we compare the results of theoretical period and experimental period, we found that they are less than 3% error, which is really close and within acceptable range. Therefore, this lab was successful and it also proved that our derived equations of the period of oscillating triangle and semi-circle were correct.