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sm_pdf_chapter8 - Chapter 8 Rotational Equilibrium and...

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Chapter 8 Rotational Equilibrium and Rotational Dynamics Quick Quizzes 1. (d). A larger torque is needed to turn the screw. Increasing the radius of the screwdriver handle provides a greater lever arm and hence an increased torque. 2. (b). Since the object has a constant net torque acting on it, it will experience a constant angular acceleration. Thus, the angular velocity will change at a constant rate. 3. (b). The hollow cylinder has the larger moment of inertia, so it will be given the smaller angular acceleration and take longer to stop. 4. (a). The hollow sphere has the larger moment of inertia, so it will have the higher rotational kinetic energy. 5. (c). The box. All objects have the same potential energy associated with them before they are released. As the objects move down the inclines, this potential energy is transformed to kinetic energy. For the ball and cylinder, the transformation is into both rotational and translational kinetic energy. The box has only translational kinetic energy. Because the kinetic energies of the ball and cylinder are split into two types, their translational kinetic energy is necessarily less than that of the box. Consequently, their translational speeds are less than that of the box, so the ball and cylinder will lag behind. 6. (c). Apply conservation of angular momentum to the system (the two disks) before and after the second disk is added to get the result: ( ) 1 1 1 2 I I I ω ω = + . 7. (a). Earth already bulges slightly at the Equator, and is slightly flat at the poles. If more mass moved towards the Equator, it would essentially move the mass to a greater distance from the axis of rotation, and increase the moment of inertia. Because conservation of angular momentum requires that const z z I ω = , an increase in the moment of inertia would decrease the angular velocity, and slow down the spinning of Earth. Thus, the length of each day would increase. 279
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280 CHAPTER 8 Answers to Even Numbered Conceptual Questions 2. If the bar is, say, seven feet above the ground, a high jumper has to lift his center of gravity approximately to a height of seven feet in order to clear the bar. A tall person already has his center of gravity higher than that of a short person. Thus, the taller athlete has to raise his center of gravity through a smaller distance. 4. The lever arm of a particular force is found with respect to some reference point. Thus, an origin for calculating torques must be specified. However, for an object in equilibrium, the calculation of the total torque is independent of the location of the origin. 6. We assume that the melt-water would form a thin shell of mass and radius around the Earth. This shell would increase Earth’s moment of inertia by an amount 19 2.3 10 kg m = × 6 6.38 10 m E R = × 2 2 3 E I mR ∆ = . If we treat Earth as a uniform solid sphere, this would represent a fractional increase of 2 2 3 2 2 5 0 5 3 E E E E mR I I M R M = = m . Thus, the fractional increase in the moment of inertial would be on the order of 19 24 10 kg 10 kg 6 10 = . In this process, angular
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