PostLab 8_ Torque

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Name : Miguel Rivera Villareal Lab/Section: Physics 180L 1009 Teaching Assistant: Nuzhat Nuari Islam Due Date: December 1st, 2022 Torque Objective: Measure the angular motion of a disk, rotating due to an applied force Apparatus: Theory: Newton’s second law of F = ma has a similar equivalent in rotational dynamics. For rotational dynamics though, the force is applied at an angle and the force that actually causes an object to spin would be the tangential component of the force. Work, and therefore power’s, formulas change to now include the angular velocity and the various angles. The force used to cause an object to spin is called torque and this can be expressed as where force is equal to the tension of the string/rope instead of mass τ = 𝐹 * 𝐷 = 𝐼 * α times gravity. In addition, torque is equal to inertia and angular acceleration. Procedure: To start the lab, level the rotational apparatus and then get a 90 cm string. Tie an end of the string to the hole in the spindle, tying the other end to the mass holder. Using calipers, find the radius of the lowest spool and the radius of the pulley. Now clamp the individual pulley to the edge of the rotational apparatus, ensuring the mass holder doesn’t hit the ground at the lowest point of its fall. Attach the smart pulley to the rotational apparatus, making sure it can freely spin when the platen spins. Add 20 grams to the mass holder and then record the total mass in the data table. Plug in the devices and link up the devices in the Pasco Capstone program. In the program, set the constant for arc length to be .015, the angle separation to be 36 degrees, enable the angular speed box (units in rad/sec), and select the graph that shows angular velocity. Now run the experiment by winding up the spool until the mass holder is below the pulley. In the program, press start when the platen is released and stop the program once a few oscillations have occurred. On the graph, highlight a linear portion and create a linear best fit.

Record this fit’s slope as the angular acceleration and then repeat the experiment by changing the mass to 50 grams, 70 grams, 170 grams. Now record the platen’s radius and mass. Using this info, calculate the moment of inertia of the disk and the angular acceleration of the platen (formula a = A * (p/r)). After recording that in the table, calculate the torque via the standard formulas and also the free body diagram formula. Then find the percent discrepancy. Equations: : torque τ ω: angular velocity α: angular acceleration

Percent Discrepancy: (τ1 − τ2)/[(τ1 + τ2 )/2] * 100 2 = I * α τ 1 = D * m (g - D * α) τ I = .5 * M *α α p = (r / p) * α α = (p / r) * α p

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Notes/Computations:

Post Lab Questions: Question 1: You probably found that Γ1 was larger than Γ2 …Why? The second torque was smaller than the first because the torque of the second utilizes the moment of inertia (I) in its equation and therefore uses the mass and angular acceleration of the disc. The end result torque for the second fails to take into account the friction that the pulley on the disc causes which counteracts/subtracts the torque. τ1 bypasses the disc and instead just uses the spindle’s information which isn’t affected by the friction that the disc undergoes. In addition to that the masses used were different: M (mass of the disc) was used for T2 while m (mass of the hangar and added) was used for T1. Question 2: How does frictional torque affect your results? Frictional torque caused the values derived from the disc’s torque to be smaller than the spindle’s torque which would have been otherwise the same in a non frictional world. Question 3: What effect did the increased mass have in the angular acceleration? An increase in mass caused an increase in angular acceleration. In terms of the graphs, the increase in mass caused the angular velocity to increase much more as time went on; a steeper slope was created. Question 4: What effect did it have on the percent discrepancy between the two torque calculations, why? The two torques, technically calculating the same torque, varied due to the mass because the masses used for each torque calculation was different; the mass used for τ1 was bigger since it included the hangar’s mass and the added while τ2 used only the disc’s mass, a constant. Question 5: When the mass is falling, which direction is the platen spinning, and which direction do the following vectors point: α ω τ… what about when the mass is going back up? When the mass is falling the platen spins counterclockwise (viewed from above) since the torque is positive. Torque is positive, according to the right hand rule, when the thumb of the hand points away from the spinning object and is negative when it points towards. A clockwise spin would mean that torque is negative which occurs when the mass is going up in the case of the lab. Angular velocity and angular acceleration both contribute to the platen’s spin, specifically the force exerted on the platen, so they also point the same direction as the torque, either outward or inward.

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