2 consider the system shown in fig 2 a pulley 1 of radius r1 and momen

Question

2. Consider the system shown in Fig. 2. A pulley 1 of radius R1 and moment of inertia I1 is connected another pulley A of radius R3 by mean of an unstrecthable belt. Pulleys A and B form a rigid body with a common hub and moment of inertia I2. a. Use the conservation of mechanical energy to find the equivalent system that can be used to replace the pulleys system (pulleys only). b. Write the kinematic equations relating the rotations between the pulleys. c. Use the equations found in a) and b) to determine the equivalent moment of inertia of the pulleys system. d. Determine the moment generated by the mass at pulley B and find the equivalent moment felt at the pulley 1. e. Write the equation of motion in terms of the angular velocity of the pulley 1 in case a moment M is applied at the shaft of the pulley 1.