Physical Pendulum Lab

Lab done on 6/7/17
Lab Partner Jonathan Goei

For this lab we are trying to calculate the moment of inertia and the period of oscillation for two shapes at two different pivot points. We will do this theoretically by taking a mathematical approach to find the moment of inertia and the period of oscillation. Then we will test this out by using a photogate to calculate the moment of inertia.

To start this experiment we had to first find the moment of inertia at the center of mass of a semicircular sheet. We then found the center of mass of this semicircular sheet. We then used this information to find the the moment of inertia at the top and bottom of the semicircle. Then using this formula we derived an equation for the angular velocity at those two spots. We then repeated these same steps for an isosceles triangle. After this we measured the base and the height of the triangle and the diameter of our semicircle in order to plug these into the equations we had derived in order to calculate the period of oscillation. Finally we compared our observed values to our theoretical values to see what our percentage of error had been.

We did a really good job of calculating the period of oscillation for these two shapes as you can see below our theoretical and experimental values were really close to each other both with a less than 1% of error. This experiment had the least percentage error than any other experiment we did during the semester.

Period of oscillation for the triangle

Period of oscillation for the semicircle

The reason why you can assume that the paper clips won't greatly affect the period of oscillation is because they are right at the axis of rotation and will therefore not affect the our moment of inertia measurements. The tape and paper are more likely to make an effect on our measured moment of inertia because they are further away from our pivot point. However, because the weight of the tape and paper is almost nothing compared to the cardboard we it wont make that great of an impact. In conclusion our experiment was a success considering we had a less than 1% in error. 

Lab 19 Conservation of Energy/ Angular Momentum

Lab Partner: Jonathan Goei
Lab Performed on 5/31/17

By doing this experiment we are trying to find the height that a piece of clay will travel to after being hit by a meter stick. We will be using conservation of energy and angular momentum to find this out.

In order to do this we first had to find the mass of the clay and the meterstick. The next thing we did was to find out what the moment of inertia of the meter stick was going to be. We did this by using the parallel axis theorem. this is because we were using a pivot at the 10 cm spot instead of the end or middle. After finding this out our next goal was to find the angular velocity of the meter stick before it collided with the piece of clay on the floor. Then we found the moment of inertia of the system, both the meter stick and the clay.After finding this out we found the angular velocity at the bottom once the clay was stuck to the meter stick. Finally we found the height that the clay rose to after it was stuck to the meterstick. We did this by using the concept that the rotational energy of the stick and clay would be conserved and turned into gravitational potential energy of the stick and clay.

 Unfortunately our theoretical results were not as close as we would have liked to our actual result. Our theoretical result said that our height should have been 0.328 m. However when we measured the height using logger pro we got .229 m. Our percentage of error was of 30%. The reason why i believe that our error was off y so much is because we messed up on the experiment and didn't drop it from a horizontal height. Another thing that could have affected our actual height is air resistance which is something that we didn't take into account when doing our theoretical approach to the problem.