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Unformatted text preview: CHAPTER 9 ROTATIONAL DYNAMICS CONCEPTUAL QUESTIONS 5. REASONING AND SOLUTION Work and torque are both the product of force and distance. Work and torque are distinctly different physical quantities, as is evident by considering the distances in the definitions. Work is defined by W = ( F cos ) s , according to Equation 6.1, where F is the magnitude of the force, is the angle between the force and the displacement, and s is the magnitude of the displacement. The magnitude of the torque is defined as the magnitude of the force times the lever arm, according to Equation 9.1. In the definition of work, the "distance" is the magnitude of the displacement over which the force acts. In the definition of torque, the distance is the lever arm, a "static" distance. The lever arm is not the same physical quantity as the displacement. Therefore, work and torque are different quantities. ____________________________________________________________________________________________ 6. REASONING AND SOLUTION A person stands on a train, both feet together, facing a window. The front of the train is to the person's left. When the train starts to move forward, a force of static friction is applied to the person's feet. This force tends to produce a torque about the center of gravity of the person, causing the person to fall backward. If the right foot is slid out toward the rear of the train, the normal force of the floor on the right foot produces a counter torque about the center of gravity of the person. The resultant of these two torques is zero, and the person can maintain his balance. ____________________________________________________________________________________________ 10. REASONING AND SOLUTION Treating the wine rack and the bottle as a rigid body, the two external forces that keep it in equilibrium are its weight, m g , located at the center of gravity, and the normal force, F N , exerted on the base by the table. Note that the weight acts at the center of gravity (CG), which must be located exactly above the point where the normal force acts, as is the case in Figure 9.10 c. m g F N CG ___________________________________________________________________________________________ 13. REASONING AND SOLUTION The space probe is initially moving with a constant translational velocity and zero angular velocity through outer space. a. When the two engines are fired, each generates a thrust T in opposite directions; hence, the net force on the space probe is zero. Since the net force on the probe is zero, there is no translational acceleration and the translational velocity of the probe remains the same. b. The thrust of each engine produces a torque about the center of the space probe. If R is the radius of the probe, the thrust of each engine produces a torque of magnitude TR, each in the same direction, so that the net torque on the probe has magnitude 2 TR . Since there is a net torque on the probe, there will be an angular acceleration. The angular velocity of the...
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