Assignment 5-11 Newport AP Physics—C. Appel Chapter 10 Problems 47. This problem describes one experimental method of determining the moment of inertia of an irregularly shaped object such as the payload for a satellite. Figure P10.47 shows a mass m suspended by a cord wound around a spool of radius r, forming part of a turntable supporting the object. When the mass is released from rest, it descends through a distance h acquiring a speed v. Show that the moment of inertia I of the equipment (including the turntable) is mr 2 2 gh v 2  1. 56. A flywheel in the form of a heavy circular disk of diameter 0.600 m and mass 200 kg is mounted on a frictionless bearing. A motor connected to the flywheel accelerates it from rest to 1,000 rev/min. (a) What is the moment of inertia of the flywheel? (b) How much work is done on it during this acceleration? (c) When the angular speed reaches 1,000 rev/min, the motor is disengaged. A friction brake is used to slow the rotational rate to 500 rev/min. How much energy is dissipated as internal energy in the friction brake? 57. A shaft is turning at 65.0 rad/s at time zero. Thereafter its angular acceleration is given by   10 rad/s 2  5t rad/s 3 , where t is the elapsed time. (a) Find its angular speed at t = 3.00 s. (b) How far does it turn in these 3 s? Chapter 11 Problems 31. A particle with a mass of 0.400 kg is attached to the 100-cm mark of a meter stick with a mass of 0.100 kg. The meter stick rotates on a horizontal, frictionless table with an angular speed of 4.00 rad/s. Calculate the angular momentum of the system when the stick is pivoted about an axis (a) perpendicular to the table through the 50.0-cm mark and (b) perpendicular to the table through the 0-cm mark. 35. A student sits on a freely rotating stool holding two weights, each of which has a mass of 3.00 kg. When his arms are extended horizontally, the weights are 1.00 m from the axis of rotation and he rotates with an angular speed of 0.750 rad/s. The moment of inertia of the student plus stool is 3.00 kg∙m2 and is assumed to be constant. The student pulls the weights inward horizontally to a position 0.300 m from the rotation axis. (a) Find the new angular speed of the student. (b) Find the kinetic energy of the rotating system before and after he pulls the weights inward. 41.  A wad of sticky clay of mass m and velocity vi is fired at a solid cylinder of mass M and radius R (Fig. P11.41). The cylinder is initially at rest and is mounted on a fixed horizontal axle that runs through the center of mass. The line of motion of the projectile is perpendicular to the axle and at a distance d, less than R, from the center. (a) Find the angular speed of the system just after the clay strikes and sticks to the surface of the cylinder. (b) Is mechanical energy conserved in this process? Explain your answer. Answers: 10-47: Proof 10-56: (a) 9.00 kg∙m2 (b) 49.3 kJ (c) -37.0 kJ 10-57: (a) 12.5 rad/s (b) 128 rad 11-31: (a) 0.433 kg∙m2/s (b) 1.73 kg∙m2/s 11-35: (a) 1.91 rad/s (b) 6.44 J 2𝑚𝑣𝑖 𝑑 11-41: (a) (𝑀+2𝑚)𝑅 2 (b) No