Work Sheet 1510 08 Rotational Dynamics

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California Polytechnic State University, Pomona *

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1510

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Physics

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Dec 6, 2023

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docx

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Lab 08 – Rotational Dynamics Please read the lab manual before doing this lab to get familiar with the procedure. Then use this worksheet to record your data shown in the video and do the calculations. Part A1: Finding the Rotational Inertia of the Disk Experimentally Setup the laser gate to get the acceleration and measure the radius R of the shaft around which the string is wrapped. Then calculate the torque using this formula: τ s = TR = m ( g a ) R Where m = M c + M a is the total mass hanging from the string. Here R = 1.513 cm. Use g = 980 cm / s 2 . Also calculate the angular acceleration using α = a / R in units of rad / s 2 . Note: The distance input to the computer should be the distance the hanging mass travels during the 7 blockages of the laser beam. This should be x = 2 πD where D = 2 R is the diameter of the shaft. So x = 2 π ( 3.026 cm ) = 19.013 cm. This should be input to the computer at the beginning of the experiment. m (g) a ( cm / s 2 ) α = a / R ( rad / s 2 ) τ s ( g.cm 2 / s 2 ) Run 1 150 0 0 232286 Run 2 250 1.538 1.016 231021 Run 3 350 2.683 1.77 379670 Run 4 450 3.595 2.376 527197 Run 5 550 4.952 3.272 674141 Run 6 650 6.156 4.068 967304 Run 7 0 -1.183 -0.782 9649.4 Now graph τ s in g.cm 2 / s 2 versus the angular acceleration α in rad / s 2 , and find the equation of line of best fit. Comparing the line of best fit on the graph with the theoretical formula τ s = + τ f What does the slope of the line represent? Rotational Inertia What is the unit of the slope? g/cm^2 What does the y-intercept represent? Frictional torque This would be the experimental value of the rotational inertia of the disk. Write this value in this table with its units. Use only four sigfigs. Experimental Rotational Inertia of the 179136
Disk I exp , for R = 1.513 cm Part A2: Finding the Rotational Inertia of the Disk Experimentally with Different R Do the same as Part A1, but this time the string is wrapped around the large disk. Then calculate the torque using this formula: τ s = TR = m ( g a ) R Where m = M c + M a is the total mass hanging from the string, and R = 10.053 cm is the radius of the disk the string is wrapped around. Use g = 980 cm / s 2 . Also calculate the angular acceleration using α = a / R in units of rad / s 2 . Note: The distance input to the computer in this case should be the distance the hanging mass travels during the 4 blockages of the laser beam. This is now x = πD where D = 2 R is the diameter of the disk. So x = π ( 20.1 cm ) = 63.15 cm. This should be input to the computer at the beginning of this experiment. m (g) a ( cm / s 2 ) α = a / R ( rad / s 2 ) τ s ( g.cm 2 / s 2 ) Run 1 50 17.102 1.701 572871 Run 2 100 38.397 3.819 1055956 Run 3 120 47.33 4.708 1242358 Run 4 150 59.92 5.960 1447556 Run 5 0 -7.849 -0.781 64550.49 Now graph τ s in g.cm 2 / s 2 versus the angular acceleration α in rad / s 2 , and find the equation of line of best fit. Paste a picture of your graph here: y = 209419x + 231356 Record your experimental value for this new R in this table with its units. Use only four sigfigs. Experimental Rotational Inertia of the Disk I exp , for R = 10.053 cm 209419
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