Rotational Motion PHYS_111 (1)

ANALYZING INERTIA: ROD AND DISK

Author(s)/Collaborators -Everett Beck, Tyler Brumbles, Matthew Bryant, Amanda Carrizo, Ivana Fernandez Rosas, Jack Franco Date 4/5/2023 Keywords Newton’s Laws, Oscillation, Pendulum, Kinetic Energy, Potential Energy, Time, Experimentation, Excel Institution Physics 111L, Department of Physics, University of Idaho, Moscow, 8384 Introduction In this lab we will expand our explorations in rotational motion and the concept of moment of inertia. We will be measuring the distance, mass, radius, weight, and the length of the rod and disk to attempt to quantify our results. We will then translate that data to calculate the moment of inertia of the object and analyze the relationship between the torque and the resulting angular acceleration and velocity of the objects. The results were then analyzed and interpreted using excel. Hypothesis  The previous knowledge gained through past labs and experiments will be used to understand and calculate centrifugal motion. By using concepts we have learned, we can integrate them into the scientific process to better understand physics, by better understanding centrifugal force.  Rotational motion according to us, can be defined as the motion produced by a force exerted on an object that is bound to a center point with a radius equivalent to the range. Procedure We started our experiment by setting up the PASCO program and proceeded to link it to the PASCO Universal Interface and the sensor. The sensor allowed us to collect the motion produced in the objects with different masses added. We measured the radius of the centered disk where we set the rotational objects and also found the radius and masses of the objects provided for the lab being the rotational motion disk and sort of a ruler like (bar), after that we proceeded to run the experiment by adding 200 kg for the first initial trial then increased by adding 200 kg for the rest of the trails a total of 4 trials. For each object we did 4 trails for the disk and for the bar motional object and kept the same weights through both experiments. Through PASCO program we were able to collect the data and observe the movement of the objects by looking at the graph produced and took the value of the angular velocity. Materials Used : • Rotary motion sensor • Rigid aluminum platform • Lightweight thread • Mass hanger and assorted masses • Scale • Bubble level • Vernier calipers • Personal computer with PASCO Capstone soft- ware Formulas  Calculation of inertia. F − d p d t Page | 3

Calculations Calculations were performed using the equations above as indicated and are as follows: Calculations for rotation with the large wheel (all values pulled from Table 2): Acceleration a M1: a = α ×R→ 3.92 × 0.02 = 0.0784 M2: a = α ×R→ 7.87 × 0.02 = 0.1574 M3: a = α ×R→ 11.8 × 0.02 = 0.236 Tension T M1: T = m× ( g − a ) → 0.2 × ( 9.81 − 0.0784 )= 1.95 M2: T = m× ( g − a ) → 0.4 × ( 9.81 − 0.1574 )= 3.86 M3: T = m× ( g − a ) → 0.6 × ( 9.81 − 0.236 )= 5.74 Torque τ M1: τ = T ×R→ 1.95 × 0.02 = 0.039 M2: τ = T ×R→ 3.86 × 0.02 = 0.078 M3: τ = T ×R→ 5.74 × 0.02 = 0.115 Expected inertia values (all values pulled from table 1 or 2): Percent error for the set (observed value pulled from the slope of graph 1): δ = | V a − V e V e | ∗ 100 → 0.0096 − 0.009 0.009 × 100 = 7.4 % Calculations for rotation with the metal bar (all values pulled from Table 3): Acceleration a M1: a = α ×R→ 3.24 × 0.02 = 0.0648 M2: a = α ×R→ 6.51 × 0.02 = 0.1302 M3: a = α ×R→ 9.79 × 0.02 = 0.1958 Tension T Page | 3 I α = 1 2 m α R 2

M1: T = m× ( g − a ) → 0.2 × ( 9.81 − 0.0648 )= 1.95 M2: T = m× ( g − a ) → 0.4 × ( 9.81 − 0.1302 )= 3.90 M3: T = m× ( g − a ) → 0.6 × ( 9.81 − 0.1958 )= 5.84 Torque τ M1: τ = T ×R→ 1.95 × 0.02 = 0.039 M2: τ = T ×R→ 3.90 × 0.02 = 0.078 M3: τ = T ×R→ 5.84 × 0.02 = 0.117 Expected inertia values (all values pulled from table 1 or 3): Percent error for the set (observed value pulled from the slope of graph 2): δ = | V a − V e V e | ∗ 100 → 0.039 − 0.024 0.024 × 100 = 63% Page | 3 I p = 1 12 m p L

Results As you can see from the tables and calculations above, we have concluded that with every passing trial the rotation speed of the metal bar and disc increases in speed and intervals due to the increasing amount of wait that is added at the beginning of each trial. Observation and Discussion Using the results we obtained through this experiment, we are able to directly compare and contrast the results to real world torque. By doing this, we can see how the results agree and disagree with the torque calculations as small discrepancies create outliers that disagree with the overall experiment. Overall the equations for torque in and out of our experiment are sound and based. Continuing forward, the results gained from this experiment can be calculated and interpreted through inertia. By showing the way rotational motion and inertia act upon the object we are able to see how inertia acts upon the object’s motion, while in a rotational motion. By keeping the object moving, inertia wants the object to move in one direction. The only thing keeping the object from moving is the friction created in between the object and the plate. Because of this the object seemingly freely rotates around the center as the disk does. Lastly, by finding the acceleration in this experiment through rotational motion, we can see how centrifugal acceleration plays a major role part in the why rotational motion. Without centrifugal acceleration we could not have obtained half of the results we gathered at the level and accuracy we achieved. This proves the existence and effectiveness of centrifugal acceleration. Conclusion We had acceptable percentages of error, meaning that our procedure was mostly accurate. The error can be contributed to human error in measurements and possibly outdated or old measuring software. We can also conclude that the greater the mass of the object on the string, the faster the angular velocity. Recommendations Being a worksheet, its relatively straight forward; although the number of formulas that were supplied for this project seem to provide a minor inconvenience due to it appearing overwhelming at first glance, if there was a way to simplify and reduce the number of formulas need or combine formulas that still accomplish the same amount of data needed for the project would help reduce the inconvenience of this problem. Contributors -Introduction  Amanda -Hypothesis  Jack -Procedure Page | 2

 Amanda  Ivanna -Materials  Tyler - Formulas  Tyler -Calculations  Matt -Results  Tyler -Observation and Discussion  Jack -Conclusion  -Recommendations  Tyler -Graphs and Tables  Matt Page | 3