Phy211 General Physics I Laboratory Instructor Tony Zable 1 Experiment Torque Rotation Objectives To compare the rotational motion of objects rolling down an incline Calculate the moment of inertia for various objects To apply the concept of torque and mechanical equilibrium to a balanced meter stick Calculate the mass of a meter stick knowing the conditions of equilibrium of a rigid body Preliminary Questions In their final appearance in the physics lab Brad and Angelina are sitting on a teeter totter Ignore the effects of friction and mass of their egos as well as that of the teeter totter a Brad with a mass of 80 kg sits 2 0 m from the fulcrum What is the torque exerted by Brad on the teeter totter b For the teeter totter to balance with Angelina sitting on the opposing end how much torque must she exert on the teeter totter c Draw a simple force vector diagram of the 2 person teeter totter system d If Angelina has a mass of 50 kg how far from the fulcrum must she sit so that the teeter totter balances e If the teeter totter is balanced does it matter where you choose the fulcrum to be when calculating the torques associated with each force exerted on it Explain Phy211 General Physics I Laboratory Instructor Tony Zable 2 A Rotational Inertia 1 Obtain a hollow cylinder a tin can with both ends cut out a solid can a full can of ravioli ought to do the trick a solid steel bearing and a hollow sphere racquetball 2 Measure the mass and radius of each object Record values in Table 1 Table 1 Initial Measurements Object Mass kg Radius R m Moment of Inertia 3 Using a collision track set up a ramp at a slight incline Measure and record the angle of the incline r 1 0 m 4 Measure a 1 0 m distance along the incline Use tape to mark the beginning and end points 5 Using a stop watch measure the time it takes for the hollow cylinder to roll 1 0 m down the ramp Record the distance and time in Table 2 6 Repeat for each object Table 2 Experimental values Object incline ralong ramp m t s aavg m s2 Phy211 General Physics I Laboratory Instructor Tony Zable 3 Question Which object reached the bottom in the shortest amount of time Arrange the objects in order time shortest to longest 7 Calculate the magnitude of the average acceleration of each object Use the following equation from kinematics aavg 2 r t2 Record the acceleration values in the table above Question Arrange the objects in order of average acceleration highest to lowest Analysis 1 Calculate the moment of inertia for the corresponding objects For these calculations assume that the mass m of each object is 0 1 kg and the radius R is 0 5 m a a solid disc b a ring or hollow cylinder c a solid sphere d a hollow sphere Phy211 General Physics I Laboratory Instructor Tony Zable 4 2 Which of the above objects has the smallest rotational inertia Arrange the objects in order their rotational inertia low to high 3 How does the order of rotational inertia values compare with the order of time and acceleration values above 4 How can you reconcile that the discrepancy between the order of the moments of inertia vs the accelerations for the various objects 5 Estimate the velocity angular velocity translational KE and rotational KE for each object at the bottom of the ramp Try using the Law of Conservation of Mechanical Energy B Mechanical Equilibrium Torque 1 Find the position of the knife edge that balances the meter stick do not weigh the meter stick ahead of time This locates the center of gravity for the meter stick 2 Attach a 200 gram mass at the 90 cm position 3 Re adjust the position of the knife edge such that the meter stick is once again balanced 200 g c g KNIFE EDGE 4 In the above diagram sketch and label the forces exerted on the meter stick Phy211 General Physics I Laboratory Instructor Tony Zable nd 5 Apply Newton s 2 5 Law to the meter stick Force Torque 6 From the conditions of mechanical equilibrium FNet 0 and Net 0 determine the mass of the meter stick and estimate the uncertainty mmeter stick of this value mmeter stick Calculated mmeter stick Estimated 7 Check this value by directly measuring the mass of the stick Calculate the error mmeter stick Measured Error 7 Calculate each torque exerted on the balanced meter stick using one end of the meter stick as the fulcrum or axis of rotation
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