3) Before understanding angular momentum, we should introduce the mechanics of it. It is similar to linear momentum; however, we will be looking at the object when it is influenced under rotational motion instead of linear motion. Since linear momentum requires some mass and velocity, so does the angular momentum. Instead of linear velocity, we will translate it to angular velocity and the point the radius when the force is exerted. So with values of the mass, radius and angular velocity, these values equal to the moment of inertia and the angular velocity. Angular momentum is still applied to the same ruled for conservation of energy. Since our lab will be experimenting inelastic collision, energy will not be conserved at some point.
4)
To understand how our apparatus works, the ball will be positioned at some height D of the inclined ramp and will slide down. Once it slides down, the ball will slide to the ball catcher and at that point, the apparatus will be influenced of angular momentum. So we know the angular momentum is the conclusion of the inelastic collision. The initial momentum will be the ball traveling under linear motion when it leaves the ramp. The ball catcher lands on the 8.1 centimeter mark from the rotating axis, and the 4.1 centimeter mark from the rotating axis. So we will be looking at two cases and compare the results of our experiment.
5) With the data we measure of the dimensions and the mass of our apparatus, here are our illustration and our theoretical results of what we expect from our experiments.
Since we know our initial inelastic momentum is the mass of the ball and the velocity, we have to solve for velocity. We placed a carbon paper on the floor and did 5 trials to measure how far the ball lands on the ground. With the dimensions we measured for height "H", we used kinematics to solve for the velocity going in the horizontal direction. We came up with 1.33 meters per second.
Once we come up with our linear velocity, our next value to solve is the moment of inertia of our apparatus. We did the same procedure similar to lab 16 to find the average angular acceleration and plug the results into the equation for moment of inertia. The radius of the apparatus will be the torque pulley and the hanging mass to be included in our equation. 
Now we are ready to solve for our theoretical conclusion for angular momentum. Our assumption for our experiment will be the initial momentum equal to final momentum. Our initial will be linear momentum and our final will be angular momentum. By the illustration provided, our results for angular velocity for two different cases is demonstrated to our prediction.
6) Now it's time to do the experiment and use logger pro to find if our prediction is correct.
This graph represents the linear velocity graph when the ball lands on the ball catcher at the 8.1 centimeter mark.
Later we derived our linear velocity and transform it to the angular velocity by using the equation linear velocity divided 8.1 centimeters. For the 4.1 centimeter mark, the graph would look exactly the same.
7)
So our theoretical conclusion came close to our experimental. But the intuition of our results makes sense. If the ball hits at the point of the radius farther than the other point of the radius that is closer to the origin, the angular velocity will rotate faster. It is the same application when pushing the door open with the same force on two different points from the origin.8) Now an additional question is asked, is energy conserved. In our experiment, at some points the energy of the ball was conserved and lost. In the beginning when the ball slid down the ramp before colliding the ball catcher, energy is conserved. It is only gravitational potential energy and kinetic energy the ball is experiencing. Of course, there is some friction when the ball slides down the ramp, but energy lost to that value is barely negligible. After the ball slides off the ramp and lands on the ball catcher, some energy is stored with the colliding mass and the angular speed decreases. So energy was lost of the concluding angular momentum.
Now gravitational potential energy and kinetic energy should be equal to each other. Some margin of error was lost. What I did to make the energy conserved was I made the linear velocity and unknown value and derived it. The linear velocity should've been around 2.3 meters per second instead of 1.33 meters per second. Since our theoretical was slightly off to our experimental, it is assumed our energy theory would be slightly off as well. But as kinetic energy from linear to rotational decreases, it is intuitive why the energy was lost.
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