Moment of Inertia
Partner: Schyler Cordova
Date: 4/11/14
Date: 4/11/14
Purpose: To determine the moment of inertia of the ring.
Theory:
The moment of inertia depends on the object and its rotational axis. Thus, different objects have different moments of inertia. The moment of inertia of the two objects in this lab are:
The moment of inertia depends on the object and its rotational axis. Thus, different objects have different moments of inertia. The moment of inertia of the two objects in this lab are:
To find the rotational inertia of the system the torques and forces need to be summed and solved for tension, T. Then, the two equations can be set equal to one another and solved for inertia, I.
Experimental Technique:
1. Mass the disk and ring.
2. Measure the radius of the disk and both the outer and inner radius of the ring. Also measure the radius of the pulley.
3. Set up the rotational motion sensor, string, disk, and ring. (See image 1)
4. Set up data studio to create a velocity versus time graph.
5. Choose a mass that will be used to accelerate the disk and ring.
6. Put the mass on the string, start data studio, and allow the mass to fall.
7. Remove the ring and repeat to find the acceleration with just the disk.
8. Use the slope of the velocity versus time graph to determine the acceleration of the disk and ring and the disk by itself.
9. Using those accelerations, calculate the moment of inertia for both the disk and the ring together as well as the moment of inertia for just the disk.
10. Use the measurements of the disk and ring to find their geometric moments of inertia.
11. Finally, compare the geometric moment of inertia to the moment of inertia calculated using the acceleration.
1. Mass the disk and ring.
2. Measure the radius of the disk and both the outer and inner radius of the ring. Also measure the radius of the pulley.
3. Set up the rotational motion sensor, string, disk, and ring. (See image 1)
4. Set up data studio to create a velocity versus time graph.
5. Choose a mass that will be used to accelerate the disk and ring.
6. Put the mass on the string, start data studio, and allow the mass to fall.
7. Remove the ring and repeat to find the acceleration with just the disk.
8. Use the slope of the velocity versus time graph to determine the acceleration of the disk and ring and the disk by itself.
9. Using those accelerations, calculate the moment of inertia for both the disk and the ring together as well as the moment of inertia for just the disk.
10. Use the measurements of the disk and ring to find their geometric moments of inertia.
11. Finally, compare the geometric moment of inertia to the moment of inertia calculated using the acceleration.
Image 1
Data:
Disk Disk and Ring
Analysis:
Rotational Inertia of Disk and Ring
Conclusion:
The purpose of this lab was to determine the moment of inertia of the ring. Using the rotational acceleration, the ring's moment of inertia was found to be .000582kgm2. The ring's geometric moment of inertia was .000507kgm2. This gave a percent difference of 13.8%. Using the rotational acceleration of just the disk, the disk's moment of inertia was found to be .000163kgm2. The disk's geometric moment of inertia was .000138kgm2. This yielded a percent difference of 16.6%. The percent differences may have been caused by friction in the pulley or rotational motion sensor.
The purpose of this lab was to determine the moment of inertia of the ring. Using the rotational acceleration, the ring's moment of inertia was found to be .000582kgm2. The ring's geometric moment of inertia was .000507kgm2. This gave a percent difference of 13.8%. Using the rotational acceleration of just the disk, the disk's moment of inertia was found to be .000163kgm2. The disk's geometric moment of inertia was .000138kgm2. This yielded a percent difference of 16.6%. The percent differences may have been caused by friction in the pulley or rotational motion sensor.
References:
Giancoli, D. C. (1998). Physics: principles with applications (5th ed.). Upper Saddle River, N.J.: Prentice Hall.
"Rotational-Linear Parallels." Moment of Inertia. N.p., n.d. Web. 22 Apr. 2014. <http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html>.
Giancoli, D. C. (1998). Physics: principles with applications (5th ed.). Upper Saddle River, N.J.: Prentice Hall.
"Rotational-Linear Parallels." Moment of Inertia. N.p., n.d. Web. 22 Apr. 2014. <http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html>.