Daniel Guzman. Lab partners( James Okamura abd Rodrigo Uribe) Physical Pendulum.

Daniel Guzman
Physical Pendulum
Physics 4A


The purpose of this experiment was to determine the period oscillations of two different geometries, one being a semicircle and the other being a isosceles triangle, to then verify using theory.

The main theoretical idea behind this particular lab is the idea of simple harmonic motion which is a very useful idea to describe oscillation motion for any object or body, in this case we used the ideas behind simple harmonic motion to find the period of oscillation for two different shapes, to do this we first had to derive an expression to find the center of mass of the shapes and after finding it we found the moment of inertia of the shapes about the point or axis that the shapes would be rotating from. Once this is done we used the equation for toque and the relationship that exists between alpha and omega to find the angular frequency, once this angular frequency is found one can use the relationship that exists between angular frequency and period to find the period of oscillation for the geometry.

The apparatus for this experiment consisted of a photo gate, a laptop, a semicircle and an isosceles triangle. The photo gate in this experiment was used to measure the period of oscillations of the two different geometries, the laptop was used to analyze and obtain the data for the period of oscillations for the two different geometries.

The experimental procedure for this lab was quite simple due that we only had to measure the period of oscillations of two geometries. The first thing that we did was to put the bodies on a clip that went through the point from which the bodies were going to oscillate after putting the clip on the geometries we made sure that the photo gate was able to record the period of oscillations of the bodies, once this was confirmed we displaced the bodies very little and then made the measurements of the period of the two bodies once this was done, the experiment is pretty much done and the only thing to do is to compare the theoretical results to the experimental ones.

Period of oscillation for the two different bodies

Period of oscillation for the semicircle

Period of oscillation for the triangle

 

Derivations for the center of mass and moment of inertia for the two geometries

Derivation for the moment of inertia of the semicircle and its center of mass

derivation for the moment of inertia of the triangle about its apex

Derivation for the center of mass the triangle

Theoretical calculations for the period of oscillation for the two geometries

Comparing the theoretical results to the experimental results (percent error)

Conclusion: the experimental results and the theoretical results were very close to each other, which means that the experiment was carried out correctly, the percent errors as shown were very small, which lets one infer that the theoretical calculations as well as the experimental procedure was done correctly. The error in this experiment was very small, which means that the error did not affect the experimental results.

lab 19: conservation of energy and conservation of angular momentum ( Daniel Guzman) lab partners James okamura and Rodrigo uribe

Daniel Guzman
Physics 4A
Conservation of energy and angular momentum


The purpose of this lab is to use the principles of angular momentum and conservation of energy to find how high a stick can go after colliding with a piece of clay that is at rest on the ground

The theory used in this experiment and particular lab is very important due that it uses two fundamental principles such as conservation of angular momentum and conservation of energy. Both of these two principles are used to find how high the clay and the stick would go; for instance, the principle of conservation of energy is used to find the angular velocity at which the stick would hit the clay that is at rest, the principle of conservation of energy is used due that the ruler is at rest is initially. after being displaced from its natural position which means that it has gained gravitational potential energy and it would be conserved in the from of kinetic energy. after the stick hits the clay and they become one body due that they stick together, we apply conservation of angular momentum, this principle can be used due that not other torque is acting on the system, which means that the momentum is conserved, using this principle we can use the initial angular velocity of the stick before hitting the clay to find the angular velocity once it hits the clay and the clay sticks to the ruler. Once again we used the principle of conservation of energy to find how high the stick would go with the clay.

Description of the apparatus
The apparatus for this experiment was quite simple it only consisted of a laptop, a meter stick, a piece of clay, a cell phone and a piece of clay. The laptop in this experiment is used to do a video analysis to determine how high the meter stick would travel with the clay. The cellphone is used to record the physical phenomena which is the piece of clay and meter stick sticking together.

The experimental procedure for this lab was the easiest from all the labs performed in this semester, due that one only needed a clamp to attached the meter stick and a bearing that would allow the meter stick rotate. After that was done one had to release the meter stick and record the collision the of the meter stick and the clay. After the video was analyzed we proceeded and apply the concepts described above to make some theoretical calculation about how high would the meter stick go.

Applying the theory described to find the maximum height that the stick travels (conservation of momentum and conservation energy used).

Comparing the theoretical results to the experimental results the percent error came up to be 14.5 %, which lets one infer that are multiple sources of error in this particular experiment or wrong assumptions were made in this experiment; for instance the pivot on which the stick is rotating is not friction-less, which we assumed it was. Another wrong assumption for this particular experiment was to assume that the mass was evenly distributed on the meter stick, which it was not because tape was added to the meter stick, which is going to change the moment of inertia and center of mass of the meter stick.

These two images let one compare the initial initial and final positions of the stick and from this graphs were would be able to compare the experimental and theoretical results

This image shows the final position of the stick from which we calculated the percent error of the experiment using the theoretical results calculated.

Conclusion: The data and results obtained for this experiment were not very accurate due that the percent error was 14.5 percent, which means that different sources of error affected the experiment. When comparing the theoretical and experimental results they were not close enough, which lets one assume that the experiment was not very accurate, and there were multiple sources of error.