Experiment 07 Angular Momentum

Introduction In this experiment we examined the concept of angular momentum, and examined it’s conservation of momentum. Angular momentum is similar to linear momentum, but has different forms of inertia, based on it’s different way of motion. Angular momentum has an inertia of rotational motion, while linear momentum has an inertia of translational motion. In angular momentum the mass and radius of the object dictates inertia, while in linear momentum it is only the mass of the object. Also, in angular momentum force is torque. Torque is a type of force that stimulates rotation. In this label there were two types of torque: frictional torque and pulling torque. Frictional torque will produce angular acceleration. Pulling torque and frictional torque will be utilized to calculate the net angular acceleration. Theory To find inertia, of a disk exhibiting angular momentum, we must include the radius of the object as well. The moment of inertia of the disk is characterized as I=1/2MR^2, where M is equal to the mass of the object and R is the radius. In the presence of a hanging mass, we observe two forces for angular momentum: frictional torque and pulling torque. These forces act upon the mass to produce a net acceleration. Net acceleration is defined as I=(mr(g-ranet))/(afr+anet). This equation is derived from the sum-of-torques on the platform and the sum-of-forces on the mass. If we have conservation of momentum, the initial angular momentum and the final angular momentum will be the same. Procedure In the first part of the experiment, we set up the photogate and measured the sum-of-torques. We did this by spinning the disk, with no mass attached for 15-20s. The data collected was velocity vs time. From this data we took the slope and got afr. After getting angular acceleration, we measured net angular acceleration. To do this we measured the radius of the spinning cylinder, and attached a 200 g mass to the spinning cylinder over a pulley. Then, we dropped the mass and collected data from the spinning disk. The data collected was velocity vs time, and from this data we were able to get the slope. The slope retrieved was net angular acceleration. For part 2 of this experiment, we measured initial angular velocity and final angular velocity. To do this, we first measured the radius and mass of the large disk. We then spun the platform, with the photogate collecting data, and then dropped the large disk with a handle a short distance on to the platform. The photogate produced a graph, in which it had a straight downward portion, a sharp drop, and then another slight downward portion. From this graph we took the last data point of the straight downward portion as the initial angular velocity and the first data point of the slight downward position as the final angular velocity. Discussions 1. Derivation of Moment of Inertia 2. Systematic Error: Handle of the Disk In calculating the mass of the disk, we ignored the mass of the handle. However, the mass of the handle will still contribute to our measurement of inertia. Mass is directly proportional to inertia. So, if our mass is greater than what we are measuring, because we ignored the handle, then inertia will be greater than what we expected. Since, inertia increases, so will our final angular momentum. This is due in part to the increase of inertia. In order to get final angular momentum, we multiplied the final angular velocity and the total momentum of inertia. 3. Systematic Error: Off-Center Drop The parallel axis theorem states that “the moment of inertia of any object about an axis through its center of mass is the minimum moment of inertia for that axis in direction in space”. In other words, if an object is moved closer to another object's center, this will reduce the moment of inertia, and increase the angular acceleration. In this case, if the disk was dropped slightly off center, this would increase the moment of inertia and decrease the angular acceleration. This is due to the fact that the disk would not be in the center of the platform's rotational axis. Results In this experiment we tested to see if the angular momentum was conserved in the collision of the disk and platform. If angular momentum was conserved initial angular momentum of the platform would equal the final angular momentum of the platform. With uncertainties in mind, our measurements of initial angular momentum and final angular momentum did not show a conservation of angular momentum. Our initial angular momentum was measured to be 0.356393388 +/- 0.006393745526 and our final angular momentum was measured to be 0.318846108 +/- 0.0084547894989. Since, the two measurements of data do not overlap to an equal value, there was no conservation of angular acceleration. Error Analysis Although we calculated uncertainties for our data measurements, there were other outside sources of error that may have contributed to the inaccuracy of our experiment For example, we didn't include the mass of the handle in our measurements. Due to this, we may have measured a lower value of inertia, because mass is directly proportional to inertia. Also, when my partner dropped the disk on the spinning platform , the disk dropped slightly off center. This also may have contributed to the error of measurements of initial and final angular momentum. Another source of error, may be the vernier calipers we used to measure the radius of the cylinder. The tool itself may not be accurate. Also we had to find the diameter of the cylinder and divide it in half to find the radius. Conclusion This experiment tested the concepts of angular momentum and its conservation of momentum.We expected momentum to be conserved, however due to sources of error our measurements did not demonstrate a conservation of momentum. Our measurements of initial and final angular momentum were 0.356393388 +/- 0.006393745526 and 0.318846108 +/0.0084547894989. These measurements do not overlap to an equal value so they don’t demonstrate the conservation of momentum. To perform this lab more accurately, we could include the handle in our measurements of mass. Also we could use a machine to drop the disk so that it drops on the center of the platform.