Rotational Inertia
1
𝐼𝜔2
2
+
1
𝑚𝑣 2
2
= 𝑚𝑔ℎ
𝑣 = 𝜔𝑟
𝐼 = 𝑚𝑟 2
2𝑔ℎ
−1
2
𝑣
Theoretical Values
Disk
Hoop
1
𝐼 = 𝑀𝑅2
2
1
𝐼 = 𝑀(𝑎2 + 𝑏 2 )
2
Equipment Data
Plastic disk
(m = 1.500 kg)
Metal hoop
(m =1.420 kg)
h=
Data tables
r=
Object
Hanging mass (kg)
Hub only
0.020
Hub only
0.020
Hub only
0.020
Hub and Disk
0.050
Hub and Disk
0.050
Hub and Disk
0.050
Hub, disk, and Ring
0.050
Hub, disk, and Ring
0.050
Hub, disk, and Ring
0.050
Average Velocity
Final Velocity (m/s)
(A) Hub only
(B) Hub and Disk
(C) Hub, Disk, and
Ring
Experimental I
Disk
B-A =
Ring
C-B-A =
Theoretical I
%error
Rotational Inertia, I
Procedure
1. Measure the dimensions of the disk and ring, and calculate the
theoretical rotational inertias of each.
2. Set up the rotational apparatus as shown, and find the velocity
of the hanging mass as it hits the ground. Do five trials each for
a. The hub with nothing mounted on it. ( Ihub )
b. The hub with the disk mounted on it. ( I
hub + Disk
)
c. The hub with the disk and ring mounted on it. ( I hub + Disk + Ring)
3. Calculate the rotational inertia for each case.
4. Use these values to determine Idisk and IRing
5. Find the percent error for each case treating the theoretical
values as the accepted values.
Lab Report Checklist
1. Data table for dimensions of the ring and disk.
2. Data table for the experimental trials.
3. 2 percent error calculations.
4. Written summary.
5. Derivation of the equation 𝐼 =
2 2𝑔ℎ
𝑚𝑟
𝑣2
−1 .