116 rotational motion - lab report PDF

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Physics 116

Section 28334

Lab Number: 11

ROTATIONAL MOTION AND MOMENT OF INERTIA Name: Abdonnie R. Holder Instructor: Doctor Sasanthi C. Peiris Partner: Aviva Lehrfield & Candy-Lynn Best Date Performed: Thursday, January 18 , 2018 th

Objective: The purpose of this lab experiment was to test various objects through a series of trials and obtain the experimental inertial constants that coincides with the theoretical inertial constants in the Vernier LabQuest 2 Computer Interfaced Version. By conducting this experiment experimenters, investigate rotational dynamic all the while, are further providing proof of Newton’s Second Law that the acceleration of an body that is being produced by a net force is

that proportional to the magnitude of the net force. Thus in accordings to Newton’s Second Law, with this experiment, students examined how the torque and moment of inertia affects the angular acceleration of a rotating body. Principle: The motion of a unyielding device is due to the consolidation of the rotation and translation to different distances of which the object makes. The rotational inertia, I, of a object that is rotating has a fixed axis that measures the resistance of the object to the angular acceleration of which the torque applies. In addition, the rotational inertia is about the axis of symmetry. The torque, , is perpendicular to the force that rotates the axis. The angular acceleration, a, is the rate of change of the angular velocity. Rotational Motion: =Ia Translational Motion: F=ma Rotational Inertia can be found by: I=KmR2 The sum of the forces producing the objects translational acceleration, a, along the ramp is given by the following equation: F=mgsin-f = ma

To find the forces that provides the object's acceleration from its center or the sum of the torques can be found by: =fR=Ia In this experiment, the object is being rolled without slipping or sliding, thus the object also has a relationship with the translational and rotational acceleration that causes this motion: =R But this is only true if: I=KmR2. Key: K is the inertial constant, whose value is dependant upon the shape of the object. Thus the value can from zero to one. M is the mass of the object. R is the radius.

When these conditions have been meet the k, inertial constant can then be found with the use of the following equation: Kexp=gsina-1 This equation is an combination of the equation to find the sum of the torques which provides the object’s acceleration and the equation that provides the rotational inertia. Using this equation, students can compare the theoretical results with the experimental to see if their experiment was successful or not. Apparatus: 1. Vernier dynamics track 2. Adjustable end stop 3. Motion detector 4. Clamp and rod support 5. Digital angle finder 6. Solid cylinder

7. Hollow cylinder

8. Solid sphere 9. Hollow sphere 10. LabQuest 2 interface 11. Logger Pro software Procedure:

1. If the experimental set up is not complete for students it must be done in the likeness of Fig 1. First students are to set up the ramp at an small angle similar to the figure above. To check to see if the ramp has been placed at the correct angle students should use the digital angle finder. Place the angle finder on top of the ramp and begin to gently move the height of the ramp until it reads a angle of 6°. 2. Next students move to the motion detector. Switch the detector on and place it to “Cart” mode. Then connect the motion detector to one of the digital ports of the LabQuest 2 device.When the connections are made, turn on the LabQuest 2 interface and connect it to the laptop. 3. When the interface is connected students are hear a faint clicking noise indicating that everything has been setup correctly. If the clicking is not heard, it must then be heard when the object is being rolled down the ramp. 4. Then, students are to open the Physics Folder. Navigate their way to PhyExpTemplates folder

and

open

the

Logger

Pro

Templates

folder.

Next

click

on

the

RotationalMotionMomentInertiaExp file. Remember that this file is made up of two pages, where the first is to collect experimenters data and the second to record and analyze data. 5. When the preliminary set-up is completed students can then begin to retrieve their objects. The items are hollow cylinder, hollow sphere, solid cylinder or solid sphere. The angle, which is 6°should be recorded within the experiment template on page two under the θ column. 6. Now, the true experiment can begin. Experimenters must keep their objects at a constant position of 115 cm which is at the very top of the ramp in front of the motion detector.

When the object is placed on the mark, have another student click to page 1 on the template. Next that student will signal when the person holding the object is to let the object roll. Simultaneously, the holder and the clicker of “Collect” on the template should begin. As the object rolls down the ramp, there should be clicking sounds that indicates that the velocity over time is being collected. 7. On the template, there is a Velocity v Time graph, select the area that has an constant acceleration. Next click the “R” to obtain the slope that will represent the acceleration of the object. The slope should be recorded on page two under the column that is labeled as a. 8. Repeat four more trials for this object and obtain the slopes. 9. Repeat steps 6 to 8 for the other objects all the while recording the slopes in their corresponding data. Experimental Data: Example Case of How K was found: Solid Sphere Trial 1: Slope: 0.7317 ms2 this slope also represents the acceleration “a” of the object. The was previously given as 6°. While the “g” is the acceleration of gravity. Kexp=gsina-1 Kexp=(9.8ms2)sin(6°)0.7317 ms2-1 Kexp= 0.399 Thus the experimental K constant inertia is relatively close to the theoretical K of 0.400. Solid Sphere

Hollow Sphere

Solid Cylinder

Hollow Cylinder

0.7317ms2 0.399

0.6125ms2 0.672

0.6833ms2 0.499

0.5182ms2 0.977

0.7289ms2 0.405

0.6205ms2 0.650

0.6784ms2 0.509

0.5164ms2 0.984

0.7156ms2 0.431

0.6156ms2 0.664

0.6751ms2 0.517

0.5269ms2 0.944

0.7223ms2 0.418

0.6218ms2 0.647

0.6794ms2 0.507

0.5188ms2 0.971

0.7088ms2 0.445

0.6166ms2 0.661

0.6822ms2 0.501

0.5207ms2 0.967

K = 0.4 theo

K = 0.67 theo

K = 0.5 theo

K = 1.00 theo

Key: Acceleration is in Italics K is in bold exp

Discussion & Conclusion: To conclude the compared to the theoretical k values, experimenters experimental should be close enough that it can be taken as accurate information. In addition, there should of been some consistency in the experiment for the experimental k values to have an close range about each other. Some mistakes that could have been made in this experiment is that when releasing the ball students may have placed their hand in front of the motion detector causing it to detect not only the objects rolling down the ramp, but the moving of the person hand causing an disrupance in the calculations. Furthermore not only does the experimental k values have to consistent, but the acceleration as well to have accurate values, without this accuracy students will have to complete the experiment all over again. Thus with accurate data and correct calculations the experimental data should coincide with Newton’s Second Law that the

acceleration of an body that is being produced by a net force that is proportional to the magnitude of the net force....