Name:



Name: Dr. Julie J. Nazareth

Assignment Partner(s): Physics 121L/131L

Date: Section:

Furlough Day Alternative Assignment - Rotational Dynamics

If you haven’t already, go and read the complete Rotational Dynamics experiment in the lab manual, including procedure. The following data was gathered by actual students doing the rotational dynamics experiment. Use the data given in Tables 1 and 3 to complete the laboratory experiment as outlined in the lab manual. Complete all of the tables and show the assigned calculations in the space provided or on an attached sheet of paper, clearly labeled. If you have any questions, ask the instructor right away!

Part A:

Table 1: Finding the Rotational Inertia Experimentally

|Mass Cup, Mc (kg) = 0.006 |Radius Smallest Disk, R (m) = 0.01505 |

|Measurement |Added Mass, |Angular |Torque |

|Description |Ma |Acceleration, |due to the string, |

| |(kg) |α (rad/s2) |τs (Nm) |

|Smallest α |0.100 |0.3405 | |

|Largest α |0.300 |1.7362 | |

|(~ 3-4 x smallest) | | | |

|Another α between |0.250 |1.4240 | |

|Another α between |0.200 |1.0225 | |

|Another α between |0.150 |0.7084 | |

|Another α between |0.125 |0.5081 | |

|No String/no added mass |0 |-0.2917 | |

Calculate the torque due to the string for the data using the mass and radius data given in Table 1 using equation 3 in your lab manual. Write your answers in the appropriate column in Table 1. Do the calculation for all of the rows of data, but show your calculation of the torque for the smallest alpha (α). Assume g = 9.80 m/s2. Remember to keep extra non-significant digits in the middle of your calculation. As always, include units.

Smallest α: τs =

Graph: Use the “linefit” program on the computer to plot τs versus α (the torque due to the string versus the angular acceleration). Torque = “y”; angular acceleration = “x”. Note whether the data is well fit by a straight line and has a positive intercept. You do NOT have to turn in a print-out of this graph. Just record the results of the graph in Table 2. An online version of the linefit program you use in the lab room can be found at

csupomona.edu/~pbsiegel/javapp/linefit.html

Table 2: Results of graph of the torque due to the string versus the angular acceleration

|Well fit by a straight |Positive Intercept? |Un-rounded |Un-rounded |

|line? | |Slope ( ) |y-intercept ( ) |

| | |± |± |

Use the slope and the y-intercept to find the experiment rotational inertia and the frictional torque. See the Theory portion of the lab manual to find out how the rotational inertia and the frictional torque are related to the slope and y-intercept. Record your results in Table 4. Don’t forget to round those numbers with uncertainty properly in Table 4!

Part B

Table 3: Measurements to Calculate the Rotational Inertia Theoretically

|Total Mass of Wheel, M (kg) = 4.876 |

|Component |Radius, |(Width) Length, |Volume of Disk, |

|Disk |R (m) |L (m) |V (m3) |

|Disk 1 |0.01505 |0.05150 | |

|Disk 2 |0.10050 |0.01600 | |

|Disk 3 |0.01505 |0.05150 | |

|Disk 4 |N/A |N/A |N/A |

Use the measurements given in Table 3 to calculate the theoretical rotational inertia from the object’s dimensions. The wheel used in the experiment consisted of only three disks, not four as shown in the figure in the lab manual. Simply ignore the terms with the number “4” as a subscript in equation 8. First, calculate the volumes of the three disks that make up the wheel. Record the volume results in Table 3. Show the volume calculation for disk 1. Then, use the calculated volumes in equation 8. Show the theoretical rotational inertia calculation (eq. 8). Record the result in Table 4. Remember to keep extra non-significant digits in the middle of your calculation. As always, include units.

Volume of disk 1: V1 =

Calculation of theoretical rotational inertia:

Itheo =

Table 4: Experimental and Theoretical Results of Experiment

|Experimental Rotational Inertia, Iexp ( |Theoretical Rotational Inertia, Itheo ( |Frictional Torque, |

|) |) |τf, ( ) |

|± | |± |

Questions:

1. Do the results of your graph support of equation 5 that was derived from Newton’s 2nd law? If your answer is “yes”, explain what specifically supports equation 5. If your answer is “no”, explain what specifically does not support equation 5. Pay close attention to the lab manual discussion of equation 5 in the Theory section.

2. Compare the experimental and theoretical values for rotational inertia, I, that you obtained in parts A and B. Do they agree within uncertainty?

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