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Prelab 1: Consider the following system consisting of a falling mass m attached by a thread to a pulley of radius r and disk/platter of rotational inertiaI. As the mass falls, the thread unwinds and spins up the platter 17 The system considered above can be used to determine the rotational inertia () of the platter and pulley Sketch the force diagram for the falling mass (m) and write the equation of motion for the mass that involves the tension (7) the weight (mg) and the downward acceleration a. b. Write the torque equation for the platter involving the tension (7) the radius () the moment of inertia (D) and the angular acceleration() c. Both equations for (a) and (b) involve the Tension (7) use substitution to eliminate the variable T. Recalling the conversion between linear and angular acceleration (a - ra) show that the algebraic work above yields: 2 You will use this result in Part I of the lab to find the rotational inertia of the main and auxiliary platters.Prelab 2: Write an expression for the conservation of energy for the system that you considered in Prelab 1. You may consider the system to be frictionless. The equations should include the change in gravitational potential energy of the falling mass (), the change in kinetic energy of the falling mass ) and the change in rotational kinetic energy of the platter (K-12l Prelab 3: In the following apparatus, the auxiliary platter is dropped onto the main platter Auxiliary Platter Spindle The m ain platter has a rotational inertia 4e and an initial angular velocity ω0. The auxiliary platter has a rotational inertia la and is initially not spinning a.) Explain why the two platters will have the same final angular velocity b.) Show that by using the conservation of angular momentum equation, the expression for the final angular velocity of the system (assuming the two carts have the same final velocity ) is described below c.) Using your answer to Part (b) above, show that the ratio of final kinetic energy to initial kinetic energy is given by the expression below Do this by noting that and that K-1/2lYou will use this result in Part III of the lab.

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au ma ma b) Fma 0 At pulleid s angular celkuahion and a s linear accelerahon ejbecomes a) ma-ma)パーエ 0. 0uupload rest of the questions separately

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