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Unformatted text preview: MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department 8.01 Physics I Fall Term 20 10 Preparation for Experiment 4, Part 1 X49 X52 X6D X79 A rotor of moment of inertia I R and outer radius R spins about a vertical axis. The rotor mount is not friction free. Rather, there is a small constant friction torque of magnitude f . A string of negligible mass is wound around the outside of the rotor. The string is attached to the rotor in a way that allows it to come free when the end is reached. The other end of the string is attached to a weight of mass m hanging from a massless frictionless pulley. When the system is released from rest the angular velocity of the rotor increases linearly at a rate 1 under the influence of the tension in the string and the torque due to friction. After the string detaches from the rotor, the rotors angular acceleration becomes 2 (a negative quantity) due to the friction torque. A qualitative graph of ( t ) is shown below. X28X74X29 X30 X74 X73X6CX6FX70X65X20X3DX20 X31 X73X6CX6FX70X65X20X3DX20 X32 a) Find expressions for I and f in terms of some or all of the quantities 1 , 2 , m , R , and g the acceleration of gravity. 1 Now imagine that the rotor is spinning down freely and at t = 0, when its angular velocity is 1 , a washer of moment of inertia I W is dropped onto it. After a time t the washer comes to rest on the rotor. At that instant they have the common angular velocity 2 . X6EX6FX74X20X72X6FX74X61X74X69X6EX67 X72X6FX74X61X74X69X6EX67X20X77X69X74X68X20X72X6FX74X6FX72 X31 X32 X49 X57 X49 X52 b) Find the moment of inertia of a uniform ring of outer radius R o , inner radius R i and total mass M . You may find it useful to recall that ( R 4 o- R 4 i ) = ( R 2 o + R 2 i )( R 2 o- R 2 i ) c) If t is so short that no angular momentum is lost to the friction torque, what is 2 in terms of I R , I W and 1 ? d) Now assume that t is long enough that the friction torque f has to be taken into account. What is 2 in terms of I R , I W , t , f and 1 ? You will make use of all of the expressions found above in performing the experiment. You can check to see if your expressions are correct by comparing them with the corresponding expressions given in the Lab Writeup. Preparation for Experiment 4, Part 2 Experiment 4 follows rather closely the situations described in Part 1. Four data files similar to those you will take in class can be found at http://web.mit.edu/8.01t/www/Prelab%20Data/....
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