June 7, 2017 Physics Pendulum Lab

Physics Pendulum Lab

By: Chris Ceron, John Choi, Amy Chung

June 7, 2017

Goal of Lab:
Derive expressions of the period of oscillation of different objects. Compare the experimental values to theoretical values.


Theory/Introduction: 
If we know the moment of inertia about a specific axis we can use what we know about simple harmonic motion to find the period of oscillation. The period is given by:



where omega is angular frequency.

Omega is a quantity we can find by using Newton's 2nd Law torque equations.
The general torque equation for this lab looks like:

The moment of inertia calculation for semi circle.

Using the data from above, we can use the parallel axis theorem to find the Inertia at the top of semi circle.

The moment of inertia for the apex of the isosceles triangle.

The pictures above show the moment of inertia derivation for the two different shapes. We use the equations found in our pre-lab to calculate the moment of Inertia around a certain point on the object

The isosceles triangle we used.

Apparatus and Procedure:

The setup shown with the semi circle

We set up a stand with a bar coming off the side to hang the object on a paper clip. We use a photogate to measure the period of the object. On the object, there is a thin strip of paper that passes through the photogate to accurately find the period.

We collect data, and give the object a small push in order to have it oscillate back and forth. We take this period and we compare it to the calculated value.

Data:

The radius of the semicircle was .105 m.
The base and height of the triangle were 0.145 m and 0.160 m respectively.

The data we obtained via LoggerPro and the photogate setup was 0.694 secs for the semicircle and 0.715 sec for the triangle.

The period for the semi circle.

The period for the isosceles triangle.

Calculated Data:

Calculations for Period using the equations mentioned in the Theory/Introduction section

The calculation for the period using the Inertia derived above. 

Conclusion:

The percent error for both cases are extremely small, both <1% (0.29% for the semicircle and 0.55% for the triangle). This shows that our derivations to find the period were accurate. Sources of error and uncertainty come from potential friction at the apex where the paper clip swings back and forth as well as usual sources such as distance measurements for radius, base and height.