Objective: The objective of this laboratory was to theoretically calculate the moment of inertia of a disk and a ring and then to verify the moment of inertia for both objects through experiment. This laboratory shows that while the theoretical is not within the uncertainty of the experimental, both values are extremely similar to each other.

Data and Analysis:

Data:

Table 1: The Angular Acceleration of No Ring and Ring

Trial No Ring Ring

5g 4.57 ± 0.005 rad/s2 1.32 ± 0.005 rad/s2

10g 13.16 ± 0.005 rad/s2 3.09 ± 0.005 rad/s2

15g 20.45 ± 0.005 rad/s2 4.83 ± 0.005 rad/s2

20g 27.89 ± 0.005 rad/s2 6.60 ± 0.005 rad/s2

25g 35.65 ± 0.005 rad/s2 8.35 ± 0.005 rad/s2 Table 2: The Average Experimental and Theoretical Moment of Inertia for No*…show more content…*

This calculation will be done later on. After using equation 1 to find the experimental moment of inertia, the average and standard deviation of the five trials for No Ring and Ring were calculated using Excel commands for average and standard deviation. The averages will be used later on in order to calculate the experimental moment of inertia for the ring. In the next step, the theoretical moment of inertia was calculated for the disk by using equation 2.

I_disk^th=1/2 M_d R_d^2 (2)

In the equation above, the I_disk^th is the theoretical moment of inertia of the disk, M_d is the mass of the disk, Rd is the radius of the disk. Next, the theoretical moment of inertia of the Ring was calculated using equation 3 below.

I_ring^th=1/2 M_r (R_1^2+R_2^2) (3)

In the equation above, I_ring^this the theoretical moment of inertia of the Ring, Mr is the mass of the ring, R_1^2 is the inner radius of the ring, and R_2^2 is the outer radius of the ring. In order to compare the experimental and theoretical moments of inertia of the Ring, the experimental moment of inertia of the ring alone has to be calculated. It is given that the experimental moment of the system equals to the experimental moment of inertia of the ring plus the experimental moment of inertia of the disk. The experimental moment of inertia can be found by solving

Data and Analysis:

Data:

Table 1: The Angular Acceleration of No Ring and Ring

Trial No Ring Ring

5g 4.57 ± 0.005 rad/s2 1.32 ± 0.005 rad/s2

10g 13.16 ± 0.005 rad/s2 3.09 ± 0.005 rad/s2

15g 20.45 ± 0.005 rad/s2 4.83 ± 0.005 rad/s2

20g 27.89 ± 0.005 rad/s2 6.60 ± 0.005 rad/s2

25g 35.65 ± 0.005 rad/s2 8.35 ± 0.005 rad/s2 Table 2: The Average Experimental and Theoretical Moment of Inertia for No

This calculation will be done later on. After using equation 1 to find the experimental moment of inertia, the average and standard deviation of the five trials for No Ring and Ring were calculated using Excel commands for average and standard deviation. The averages will be used later on in order to calculate the experimental moment of inertia for the ring. In the next step, the theoretical moment of inertia was calculated for the disk by using equation 2.

I_disk^th=1/2 M_d R_d^2 (2)

In the equation above, the I_disk^th is the theoretical moment of inertia of the disk, M_d is the mass of the disk, Rd is the radius of the disk. Next, the theoretical moment of inertia of the Ring was calculated using equation 3 below.

I_ring^th=1/2 M_r (R_1^2+R_2^2) (3)

In the equation above, I_ring^this the theoretical moment of inertia of the Ring, Mr is the mass of the ring, R_1^2 is the inner radius of the ring, and R_2^2 is the outer radius of the ring. In order to compare the experimental and theoretical moments of inertia of the Ring, the experimental moment of inertia of the ring alone has to be calculated. It is given that the experimental moment of the system equals to the experimental moment of inertia of the ring plus the experimental moment of inertia of the disk. The experimental moment of inertia can be found by solving

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