**Unformatted text preview: **PHY 122: Rotational Motion
Kyle Kas
Branson, Tyler
Friday 10:00AM-11:50AM
TA: Ankush Objective Section:
The objective of this lab was to understand angular acceleration, torque, and moment of
inertia for a system of a mass hanging from a pulley.
Experimental Data:
Mass of Block = 0.4432 kg
Mass of hanging weight = 0.020 kg
Dimensions of block = 0.050 m x 0.040 m x 0.030 m
Radius of Small Pulley = 0.0048 m
Radius of Medium Pulley = 0.0143 m
Short axis
Small pulley
Medium pulley
Angular
acceleration
Initial angular
position
Initial angular
velocity
Final angular
position
Final angular
velocity Long axis
Small pulley
Medium pulley 6.69 rad/s2 17.4 rad/s2 10.8 rad/s2 27.6 rad/s2 0 0 0 0 0 0 0 0 140.848 rad 55.519 rad 153.764 rad 52.587 rad 42.76 rad/s 42.76 rad/s 55.5 rad/s 53.06 rad/s Data Analysis Section:
Static moment of inertia 1
( + )
12
For the short axis:
= (0.4432 )((0.050
= 1.514 ∗ 10
For the long axis:
= (0.4432 )((0.040
= 9.233 ∗ 10
Error for static moment of inertia
= ∆ = ∗∆ + ∗∆ + ) + (0.040 ) ) ) + (0.030 ) ) ∗∆ ∆ = ( 12 + 12 )∗∆ + ( 6 )∗∆ + ( 6 )∗∆ For the short axis:
∆
= ( (0.050 )
(0.040 )
+
) ∗ (0.00001
12
12 ) + ( (0.4432 )(0.050
6 ) ) ∗ (0.00005 ) + ( ) ∗ (0.00005 ) + ( (0.4432 )(0.040
6 ) (0.4432 )(0.030
6 ) ) ∗ (0.00005 ) ) ∗ (0.00005 ) ∆ = 2.4 ∗ 10
For the long axis:
∆
= ( (0.040 )
(0.030 )
+
) ∗ (0.00001
12
12 ) + ( ∆ (0.4432 )(0.040
6 ) = 1.8 ∗ 10 Dynamic moment of inertia − =
For short axis and small pulley
= (0.020 = (0.020 = (0.020 = (0.020 )(0.0048 ) 9.8 − (0.0048 )(6.69 ) )(17.4 ) )(10.8 ) )(27.6 ) 6.69
For short axis and medium pulley
)(0.0143 ) 9.8 − (0.0143 17.4
For long axis and small pulley
)(0.0048 ) 9.8 − (0.0048 10.8
For long axis and medium pulley
)(0.0143 ) 9.8 − (0.0143
27.6 Error in dynamic moment of inertia
∆
∆ = =
( ( For short axis and small pulley ∗∆
− )) ∗ ∆ = 1.4017 ∗ 10 = 1.5699 ∗ 10 = 8.6650 ∗ 10 = 9.7561 ∗ 10 ∆ = ((0.0048 9.8 − (0.0048 ) ) 6.69 ) ∗ (0.00001 6.69 ) = 7.0 ∗ 10 For short axis and medium pulley
∆ = (0.0143 ) 9.8 − (0.0143 )(17.4 ) 17.4 ∗ 0.00001 = 7.8 ∗ 10 ∗ 0.00001 = 4.3 ∗ 10 ∗ 0.00001 = 4.9 ∗ 10 For long axis and small pulley
∆ = (0.0048 ) 9.8 − (0.0048 )(10.8 ) 10.8 For long axis and medium pulley
∆ = (0.0143 ) 9.8 − (0.0143 )(27.6 ) 27.6 Results Section:
Static moment of inertia:
Short axis
Long axis (1.514 0.002)*10-4 kg m2
(9.23 0.02)*10-5 kg m2 Dynamic moment of inertia:
Short axis small pulley
Short axis medium pulley
Long axis small pulley
Long axis medium (1.4017 0.0007)*10-4 kg m2
(1.5699 0.0008)*10-4 kg m2
(8.665 0.004)*10-5 kg m2
(9.756 0.005)*10-5 kg m2 = −2.424 ∗ 10
Discussion and Conclusion Section:
The objective of this lab was to understand angular acceleration, torque, and moment of
inertia for a system of a mass hanging from a pulley.
The concepts studied in this lab are angular acceleration, moment of inertia and torque.
Angular acceleration is the rate of change of angular velocity and is usually measured in
rad/s2. Moment of inertia is a body’s tendency to resist angular acceleration. Torque is the
likeliness that a force will cause an object to rotate. At the beginning of the lab the metal block’s dimensions and mass were measured. Then
the block was put on the rotary through its short axis, and the mass was wound up on the
medium pulley. Then the mass was let go with the sensors recording data to the program.
Then this process was repeated but with the mass wound around the smaller pulley. Then
the block was placed on the rotary through the long axis and the process was repeated.
The results came out quite well. The calculated static moment of inertia and the dynamic
moment of inertia were very close to each other. Also the torque value was close to what
was expected.
Some possible sources of error could be setting up the equipment wrong. Another
possible source is not using the program right to acquire data. Error could also happen in
calculations.
The data we received in the lab was good and what was expected. The dynamic and static
moments of inertia were very close to each other. Therefore, the objective of this
experiment has been accomplished with victory! ...

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