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# lab 8 - TORQUE AND INERTIA Objective The purpose of this...

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18 TORQUE AND INERTIA Objective : The purpose of this experiment is to study torque in a dynamic situation and obtain a better understanding of moment of inertia. Apparatus : Cenco centripetal force apparatus with moment of inertia accessory, masses, Computer, Calipers, micrometer, (use short string so mass hangs about 10 cm off the floor). Background : The purpose of this lab is to compare the moment of inertia calculated from rotational acceleration caused by a known torque to that predicted by the direct moment of inertia calculation. The equations describing the motion of rotating bodies under constant torque are very similar to the equations of motion for constant linear acceleration. Replacing the mass with the moment of inertia and also the force with the torque gives the equations for the angular motion quantities. So, the sum of all forces on an object, F ma , becomes I Eq 1) where is the sum of all torques, I is the moment of inertia, and is the angular acceleration. The other rotational motion equations are similar to the linear motion equations as well. These can be solved for by integrating equation 1. The results are 0 0 I t t , and Eq 2) 0 0 2 0 0 2 1 2 1 2 t I t t t . Eq 3) Linear quantities are related to the circular quantities using the following equations, d R , Eq 4) v R , and Eq 5) a R Eq 6) where v is the speed, is the angular velocity, R is the radius of motion, d is the circumference displacement and is the angular displacement. The torque need not be applied at the radius where the masses are located so it is designated to have a different r . The torque when the force is applied perpendicular to the radius is given by Fr . Eq 7) Using the example of a me rry go round, one can understand immediately why the r’s can be different. The torque need not be applied out where the horses are; it can be applied to a central

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